Question

How do you find the sum of the first 8 terms of the geometric series 10 + 15 + 22.5 + ...?

Answer 1

492.6 ( 1 decimal place )

Explanation:

for this geometric series the first term a = 10 n = 8 and common ratio r = `15/10 = 1.5`

the sum to n terms is found by using the following formula

`color(red)( S_n =( a(r^n - 1 ))/(r - 1 ) ( r ≠1)`

`rArr S_8 =( 10( 1.5^8 - 1 ))/(1.5 - 1`

`rArr S_8 = 246.289/0.5 = 492.6`