Question

How do you find the sum of the first 10 terms of the following geometric sequence 5, 10, 20, 40, 80, …….?

Answer 1

`5115`

Explanation:

`a_0=5`
`r=2`

We are asked for the sum of the first 10 terms i.e. `a_0, a_1, ..., a_9`
so `n=9` in the general geometric sum formula:
`color(white)("XXX")Sigma_(i=0)^n = a_0*(1-r^(n+1))/(1-r)`

In this case we have
`color(white)("XXX")Sigma_(i=0)^9 = 5*(1-2^10)/(1-2) = 5xx1023=5115`