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

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 



Thus, rearranging this, we have



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

a = S(1 - r)

Lie