Question

How do you find `a_1` for the geometric series given `S_n=1530`, r=2, n=8?

Answer 1

`a_1=6`

Explanation:

In a Geometric series `n^(th)` term of the series `S_n`, where `|r|>1` is given by `S_n=a_1(r^n-1)/(r-1)`.

Here `S_n=1530`, `r=2` and `n=8` and as such

`1530=(a_1×(2^8-1))/(2-1)`

= `(a_1×255)/(2-1)`

= `a_1×255`

Hence, `a_1=1530/255=6`.