1) Evaluate the geometric series described: −5, 15, −45, 135, −405, ..., n = 7
r = 15−5 = −3
Sn = a(rn − 1)r − 1 = −5((−3)7 − 1)−3 − 1 = −5(−2187 − 1)−3 − 1 = 2735
2) Evaluate the geometric series described: 9, 18, , 36, 72, ..., n = 9
r = 189 = 2
Sn = a(rn − 1)r − 1 = 9(29 − 1)2 − 1 = 9(512 − 1) = 4599
3) Evaluate the geometric series described: ∑n = 9n = 1 7(−2)n − 1
∑n = 9n = 1 7(−2)n − 1 ⇒ r = −2, a = 7
Sn = a(rn − 1)r − 1 = 7((−2)9 − 1)−2 − 1 = 7(−512 − 1)−3 = 1197
4) Evaluate the geometric series described: ∑n = 5n = 1 5(3)n − 1
∑n = 5n = 1 5(3)n − 1 ⇒ r = 3, a = 5
Sn = a(rn − 1)r − 1 = 5(35 − 1)3 − 1 = 5(243 − 1)2 = 605
5) Evaluate the geometric series described: ∑n = 6n = 1 3(−12)n − 1
∑n = 6n = 1 3(−12)n − 1 ⇒ r = −12 , a = 3
Sn = a(rn − 1)r − 1 = 3((−12)5 − 1)−12 − 1 = 3(−132 − 1)−32 = 6632 = 3316
6) Evaluate the geometric series described: ∑n = 4n = 1 8(13)n − 1
∑n = 4n = 1 8(13)n − 1 ⇒ r = 13 , a = 8
Sn = a(rn − 1)r − 1 = 8((13)4 − 1)13 − 1 = 8(181 − 1)−23 = 32027
7) Evaluate the geometric series described: 1, 4, 16, 64, 256, ..., n = 6
r = 41 = 4
Sn = a(rn − 1)r − 1 = 1((4)6 − 1)4 − 1 = 4096 − 13 = 1365
8) Evaluate the geometric series described: 1024, 256, 64, 16, 4, ..., n = 6
r = 2561024 = 14
Sn = a(rn − 1)r − 1 = 1024((14 )6 − 1)14 − 1 = 1024(14096 − 1−34 = 1365
9) Evaluate the geometric series described: 7, 14, 28, 56, 112, ..., n = 4
r = 147 = 2
Sn = a(rn − 1)r − 1 = 7((2)4 − 1)2 − 1 = 7(16 − 1) = 105
10) Evaluate the geometric series described: 54, 18, 6, 2, 23, ..., n = 4
r = 1854 = 13
Sn = a(rn − 1)r − 1 = 54((13)4 − 1)13 − 1 = 80