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

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

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