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All Textbook Solutions for Intermediate Algebra
In the following exercises, expand each binomial. 223. (5x2y)4In the following exercises, expand each binomial. 224. (2x+5y)4In the following exercises, expand each binomial. 225. (3x+4y)5In the following exercises, find the indicated term in the expansion of the binomial. 226. Sixth term of (x+y)10In the following exercises, find the indicated term in the expansion of the binomial. 227. Fifth term of (a+b)9In the following exercises, find the indicated term in the expansion of the binomial. 228. Fourth term of (xy)8In the following exercises, find the indicated term in the expansion of the binomial. 229. Seventh term of (xy)11In the following exercises, find the coefficient of the indicated term in the expansion of the binomial. 230. y3 term of (y+5)4In the following exercises, find the coefficient of the indicated term in the expansion of the binomial. 231. x6 term of (x+2)8In the following exercises, find the coefficient of the indicated term in the expansion of the binomial. 232. x5 term of (x4)6the following exercises, find the coefficient of the indicated term in the expansion of the binomial. 233. x7 term of (x3)9In the following exercises, find the coefficient of the indicated term in the expansion of the binomial. 234. a4b2 term of (2a+b)6the following exercises, find the coefficient of the indicated term in the expansion of the binomial. 235. p5q4 term of (3p+q)9your own words explain how to find the rows of the Pascal's Triangle. Write the first five rows of Pascal's Triangle.In your own words, explain the pattern of exponents for each variable in the expansion of.In your own words, explain the difference between (a+b)n and (ab)n.your own words, explain how to find a specific term in the expansion of a binomial without expanding the whole thing. Use an example to help explain.In the following exercises, write the first five terms of the sequence whose general term is given. 240. an=7n5the following exercises, write the first five terms of the sequence whose general term is given. 241. an=3n+4In the following exercises, write the first five terms of the sequence whose general term is given. 242. an=2n+nIn the following exercises, write the first five terms of the sequence whose general term is given. 243. an=2n+14nIn the following exercises, write the first five terms of the sequence whose general term is given. 244. an=( 1)nn2In the following exercises, find a general term for the sequence whose first five terms are shown. 245. 9,18,27,36,45,...In the following exercises, find a general term for the sequence whose first five terms are shown. 246. 5,4,3,2,1,...In the following exercises, find a general term for the sequence whose first five terms are shown. 247. 1e3,1e2,1e,1,e,...In the following exercises, find a general term for the sequence whose first five terms are shown. 248. 1,8,27,64,125,...In the following exercises, find a general term for the sequence whose first five terms are shown. 249. 13,12,35,23,57,...In the following exercises, using factorial notation, write the first five of the sequence whose general term is given. 250. an=4n!In the following exercises, using factorial notation, write the first five of the sequence whose general term is given. 251. an=n!(n+2)!In the following exercises, using factorial notation, write the first five of the sequence whose general term is given. 252. an=(n1)!( n+1)2In the following exercises, expand the partial sum and find its value. 253. i=17(2i5)In the following exercises, expand the partial sum and find its value. 254. i=135iIn the following exercises, expand the partial sum and find its value. 255. k=044k!In the following exercises, expand the partial sum and find its value. 256. k=14(k+1)(2k+1)In the following exercises, write each sum using summation notation. 257. 13+19127+1811243In the following exercises, write each sum using summation notation. 258. 48+1216+2024In the following exercises, write each sum using summation notation. 259. 4+2+43+1+45In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference. 260. 1,2,4,8,16,32,...In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference. 261. 7,1,5,11,17,23,...In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference. 262. 13,9,5,1,3,7,...In the following exercises, write the first five terms of each arithmetic sequence with the given first term and common difference. 263. a1=5 and d=3In the following exercises, write the first five terms of each arithmetic sequence with the given first term and common difference. 264. a1=8 and d=2In the following exercises, write the first five terms of each arithmetic sequence with the given first term and common difference. 265. a1=13 and d=6In the following exercises, find the term described using the information provided. 266. Find the twenty-fifth term of a sequence where the first term is five and the common difference is three.In the following exercises, find the term described using the information provided. 267. Find the thirtieth term of a sequence where the first term is 16 and the common difference is -5.In the following exercises, find the term described using the information provided. 268. Find the seventeenth term of a sequence where the first term is -21 and the common difference is two.In the following exercises, find the indicated term and give the formula for the general term. 269. Find the eighteenth term of a sequence where the fifth term is 12 and the common difference is seven.In the following exercises, find the indicated term and give the formula for the general term. 270. Find the twenty-first term of a sequence where the seventh term is 14 and the common difference is -3.In the following exercises, find the first term and common difference of the sequence with the given terms. Give the formula for the general term. 271. The fifth term is 17 and the fourteenth term is 53.In the following exercises, find the first term and common difference of the sequence with the given terms. Give the formula for the general term. 272. The third term is -26 and the sixteenth term is -91.In the following exercises, find the sum of the first 30 terms of each arithmetic sequence. 273. 7,4,1,2,5,...In the following exercises, find the sum of the first 30 terms of each arithmetic sequence. 274. 1,6,11,16,21,...In the following exercises, find the sum of the first fifteenth term of the arithmetic sequence whose general term is given. 275. an=4n+7In the following exercises, find the sum of the first fifteenth term of the arithmetic sequence whose general term is given. 276. an=2n+19In the following exercises, find each sum. 277. i=150(4i5)In the following exercises, find each sum. 278. i=130(3i7)In the following exercises, find each sum. 279. i=135(i+10)In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio. 280. 3,12,48,192,768,3072,...In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio. 281. 5,10,15,20,25,30,...In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio. 282. 112,56,28,14,7,72,...In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio. 283. 9,18,36,72,144,288,...In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio. 284. a1=3 and r=5In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio. 285. a1=128and r=14In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio. 286. a1=5 and r=3In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given. 287. Find a9 given a1=6 and r=2.In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given. 288. Find a11 given a1=10,000,000 and r=0.1.In the following exercises, find the indicated term of the given sequence. Find the general term of the sequence. 289. Find a12 of the sequence, 6,24,96,384,1536,6144,...In the following exercises, find the indicated term of the given sequence. Find the general term of the sequence. 290. Find a9 of the sequence, 4374,1458,486,162,54,18,...In the following exercises, find the sum of the first fifteen terms of each geometric sequence. 291. 4,8,16,32,64,128...In the following exercises, find the sum of the first fifteen terms of each geometric sequence. 292. 3,12,48,192,768,3072...In the following exercises, find the sum of the first fifteen terms of each geometric sequence. 293. 3125,625,125,25,5,1...In the following exercises, find the sum 294. i=187(3)iIn the following exercises, find the sum 295. i=1624( 1 2 )iIn the following exercises, find the sum of each infinite geometric series. 296. 113+19127+1811243+1729...In the following exercises, find the sum of each infinite geometric series. 297. 49+7+1+17+149+1343+...In the following exercises, write each repeating decimal as a fraction. 298. 0.8In the following exercises, write each repeating decimal as a fraction. 299. 0.36In the following exercises, solve the problem. 300. What is the total effect on the economy of a government tax rebate of $360 to each household in order to stimulate the economy if each household will spend 60% of the rebate in goods and services?In the following exercises, solve the problem. 301. Adam just got his first full-time job after graduating from high school at age 17. He decided to invest $300 per month in an IRA (an annuity). The interest on the annuity is 7% which is compounded monthly. How much will be in Adam's account when he retires at his sixty-seventh birthday?In the following exercises, expand each binomial using Pascal’s Triangle. 302. (a+b)7In the following exercises, expand each binomial using Pascal’s Triangle. 303. (xy)4In the following exercises, expand each binomial using Pascal’s Triangle. 304. (x+6)3In the following exercises, expand each binomial using Pascal’s Triangle. 305. (2y3)5äIn the following exercises, expand each binomial using Pascal’s Triangle. 306. (7x+2y)3In the following exercises, evaluate. 307. (a) ( 111) (b) ( 12 12) (c) ( 130) (d) (83)In the following exercises, evaluate. 308. (a) (71) (b) (55) (c) (90) (d) (95)In the following exercises, evaluate. 309. (a) (11) (b) ( 15 15) (c) (40) (d) ( 112)In the following exercises, expand each binomial, using the Binomial Theorem. 310. (p+q)6In the following exercises, expand each binomial, using the Binomial Theorem. 311. (t1)9In the following exercises, expand each binomial, using the Binomial Theorem. 312. (2x+1)4In the following exercises, expand each binomial, using the Binomial Theorem. 313. (4x+3y)4In the following exercises, expand each binomial, using the Binomial Theorem. 314. (x3y)5In the following exercises, find the indicated term in the expansion of the binomial. 315. Seventh term of (a+b)9In the following exercises, find the indicated term in the expansion of the binomial. 316. Third term of (xy)7In the following exercises, find the coefficient of the indicated term in the expansion of the binomial. 317. y4 term of (y+3)6In the following exercises, find the coefficient of the indicated term in the expansion of the binomial. 318. x5 term of (x2)8In the following exercises, find the coefficient of the indicated term in the expansion of the binomial. 319. a3b4 term of (2a+b)7In the following exercises, write the first five terms of the sequence whose general term is given. 320. an=5n33nIn the following exercises, write the first five terms of the sequence whose general term is given. 321. an=(n+2)!(n+3)!Find a general term for the sequence, 23,45,67,89,1011,...Expand the partial sum and find its value. i=14( 4)iWrite the following using summation notation. 1+1419+116125Write the first five terms of the arithmetic sequence with the given first term and common difference. a1=13 and d=3Find the twentieth term of an arithmetic sequence where the first term is two and the common difference is -7.Find the twenty-third term of an arithmetic sequence whose seventh term is 11 and common difference is three. Then find a formula for the general term.Find the first term and common difference of an arithmetic sequence whose ninth term is -1 and the sixteenth term is -15. Then find a formula for the general term.Find the sum of the first 25 terms of the arithmetic sequence, 5,9,13,17,21,...Find the sum of the first 50 terms of the arithmetic sequence whose general term is an=3n+100.Find the sum. i=140(5i21)In the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio 332. 14,3,8,19,30,41,...In the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio 333. 324,108,36,12,4,43,...In the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio 334. Write the first five terms of the geometric sequence with the given first term and common ratio. a1=6 and r=2In the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio 335. In the geometric sequence whose first term and common ratio are a1=5 and r=4, find a11.In the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio 336. Find a10 of t he geometric sequence, 1250,250,50,10,2,25,.... Then find a formula for the general term.the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio 337. Find the sum of the first thirteen term of the geometric sequence, 2,6,18,54,162,486...In the following exercises, find the sum. 338. i=195(2)iIn the following exercises, find the sum. 339. 115+1251125+162513125+...In the following exercises, find the sum. 340. Write the repeating decimal as a fraction. 0.81In the following exercises, find the sum. 341. Dave just got his first full-time job after graduating from high school at age 18. He decided to invest $450 per month in an IRA (an annuity). The interest on the annuity is 6% which is compounded monthly. How much will be in Adam's account when he retires at his sixty-fifth birthday?In the following exercises, find the sum. 342. Expand the binomial using Pascal’s Triangle. (m2n)5In the following exercises, find the sum. 343. Evaluate each binomial coefficient (a) (81) (b) ( 16 16) (c) ( 120) (d) ( 106)In the following exercises, find the sum. 344. Expand the binomial using the Binomial Theorem. (4x+5y)3