Question

Question 17

O Mark this
Find the sum of the first 10 terms of the following geometric sequences:
{3, 6, 12, 24, 48...}
3069
3066
O
3072
O 3075

Answer 1

`S_(10) = 3069`

Explanation:

Given

`Sequence = \{3, 6, 12, 24, 48...\}`

Required

Determine the sum of the first terms

First, we calculate the common ratio (r)

`r = (T_2)/(T_1)`

`r = (6)/(3)`

`r = 2`

The required sum is:

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

Substitute 3 for a, 2 for r and 10 for n

`S_(10) = (3(2^(10)-1))/(2-1)`

`S_(10) = (3(1024-1))/(2-1)`

`S_(10) = (3(1023))/(2-1)`

`S_(10) = (3(1023))/(1)`

`S_(10) = (3069)/(1)`

`S_(10) = 3069`