Question

in the GP . 0.15, 0.015, 0.0015, ........ find the sum of 8 terms​

Answer 1

Answer:

Sum of 8 terms is 0.166666665

Step-by-step explanation:

GP series is given as

0.15, 0.015, 0.0015,......

Sum of n numbers in geometric progression is given as

When r < 1, then sum is Sn = a.(1 - r^n)/(1 - r)

When r> 1, then sum is Sn = a.(r^n - 1)(r - 1)

Here, in GP,

a = 0.15

r = 0.015/0.15 = 0.1

Also, r < 1

Thus, sum of first 8 terms in calculated as

S8 = a.(1 - r^n)/(1 - r)

S8 = 0.15(1- 0.1^8)/(1 - 0.1)

S8 = 0.15(1 - 0.00000001)/(0.9)

S8 = (0.15 * 0.99999999)/0.9

S8 = 0.15 * 1.1111111

S8 = 0.166666665