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
[tex] S = \frac{a}{(1 - r)} [/tex]
Thus, rearranging this, we have
[tex] a = S(1 - r) [/tex]
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)
