Question

Find the sum of the first 7 terms of the following series, to the nearest integer. 15,3, 3/5

Answer 1

Answer:

19

Step-by-step explanation:

This is a geometric series.

15, 3, (3/5), ...

common ratio r = 3/15 = (1/5)

a_1 = 15

Formula for nth term:   a_n = a_1 * r^(n-1)

a_n  = 15 *(1/5)^(n - 1)

We want the sum of the first 7 terms.

S =  a_1 * ( r^n  - 1) / (r - 1)

here let n = 7

S = 15 *  ( (1/5)^7 - 1 ) / ( (1/5) - 1)

S = 15 * ( (1/5)^7 - 1)  / (-4/5)

S = 15 * (5/-4) * ( (1/5)^7 - 1)

S =  ( -75/4 )* (-0.9999872)

S = - (-18.74976)  =  18.749...

The sum is about   19