Question

How to find the first term in an infinite geometric series?

Answer 1

First, we must check if the geometric series presented has an infinite sum by making sure that the common ratio, r, meets the condition that | r | < 1.

If so, to find the first term, a, we must recall that the sum of an infinite geometric series can be expressed as 

$S = \frac{a}{(1 - r)}$

Thus, rearranging this, we have

$a = S(1 - r)$

Therefore, to find the first term of an infinite geometric series, we must multiply the sum and the to (1 - r).

Answer: a = S(1 - r)