What is the sum of a 22-term arithmetic sequence where the first term is 56 and the last term is -28?

1. (1/2)(56-28)*22 = 308

Answer: C

2. 4(-5)^6 = 62,500

Answer: C

2. a9 = a1 * r^8 = -8 (8192/8)^(8/5) = -524,288

Answer: D

1). What's the sum of the geometric sequence 3, 15, seventy five, … if there are eight phrases? 292,968 2). What is the 7th term of the geometric sequence 4, –20, a hundred, …? –312,500 –12,500 sixty two,500 1,562,500 three). What's the thirty second term of the arithmetic sequence where a1 = 15 and a13= –57? –171 –one hundred sixty five –159 –151 4). What's the fifteenth term of the arithmetic sequence 17, 24, 31, … ? 108 115 122 129 5). What is the ninth term of the geometric sequence where a1 = –7 and a6 = –7,168? –327,680 –393,216 –458,752 –524,288 6). What's the 9th time period of the geometric sequence three, 9, 27, …? 2,187 6,561 19,683 59,049 7). What is the sum of a 7–term geometric sequence if the first time period is –6, the last term is –24,576, and the usual ratio is 4? –32,766 –19,662 19,662 32,766 eight). What is the sixth time period of the geometric sequence the place a1 = 625 and a2 = –125? –zero.2 0.04 –0.04 0.2 9). What's the thirty second time period of the arithmetic sequence where a1 = –32 and a9 = –a hundred and twenty? –384 –373 –362 –351 10). What's the eighth term of the geometric sequence where a1 = 256 and a3 = 16? Zero.125 zero.0625 zero.03125 0.015625 eleven). What is the sum of the geometric sequence 1, –6, 36, … if there are 6 terms? –39,991 6,665 –6,665 39,991 12). What is the sum of the arithmetic sequence 308, 304, 300, …, if there are 25 terms? 6,450 6,475 6,500 6,525 13). What is the twenty third term of the arithmetic sequence the place a1 = 7 and a5 = 21? 77 84 91 ninety eight 14). What's the sum of a 56–time period arithmetic sequence where the first time period is 6 and the last time period is 391? 10,719 11,116 11,513 eleven,910 15). What's the sum of the arithmetic sequence 153, 139, 125, …, if there are 22 phrases? 132 154 176 198 16). What is the sum of a 6–time period geometric sequence if the primary term is 22 and the last time period is 1,299,078? 1,395,030 1,461,460 1,527,890 1,594,320 17). What is the sum of a 22–term arithmetic sequence where the primary time period is fifty four and the final term is –30? 264 288 312 336 18). What is the sum of the arithmetic sequence 9, 14, 19, …, if there are 38 terms? Three,743 3781 three,819 3,857 19). On the finish of the primary day, 7 weeds appear to your regional park. On a daily basis, the number of weeds increases through 4 occasions. How many weeds will probably be in the park at the finish of 14 days? 35,456,231 626,349,395 seventy one 392 20). What's the 30th time period of the arithmetic series 2, 5, eight, … ? 89 88 87 86

m + d = 56

m + 22d = -28

m + 22d - m - d = -28 - 56

21d = -84

d = -4

m - 4 = 56

m = 60

60 - 4 + 60 - 2 * 4 + 60 - 3 * 4 + ... + 60 - 22 * 4 =>

60 * 22 - 4 * (1 + 2 + 3 + 4 + ... + 22) =>

60 * 22 - 4 * 22 * 23 / 2 =>

22 * (60 - 2 * 23) =>

22 * (60 - 46) =>

22 * 14 =>

308

-20 / 4 = -5

4 * (-5)^(7 - 1) =>

4 * (-5)^6 =>

4 * 25^3 =>

4 * 15625 =>

62500

a[6] = m * r^6

a[1] = m * r^1

m * r^6 / (m * r) => r^5

r^5 = (-8192 / -8)

r^5 = 1024

r^5 = (+/- 4)^5

r = +/- 4

-8 = -4m , 4m

m = 2 , -2

a[9] =>

m * r^9 =>

2 * (-4)^9 , -2 * (4)^9

-2 * 4^9 =>

-2 * 2^18 =>

-2^19 =>

-2^20 / 2 =>

-1048576 / 2 =>

-524288