Question

The first term in a geometric series is 5 and the common ratio is 2. Find the sum of the first 10 terms in the series.

Answer 1

5115

Explanation:

The sum to n terms of a geometric sequence is

`S_(n)` =
`(a((r^(n))-1) )/(r-1)`

where a is the first term and r the common ratio

Here a = 5 and r = 2 , thus

`S_(10)` =
`(5(2^(10)-1) )/(2-1)` = 5 (1024 - 1) = 5 × 1023 = 5115