Back to Derive geometric series formula — Problem 5 · Task Set 8

Exercises: Geometric Series Formula

For each problem, identify the parameters a, r, and n before applying any formula. Always check whether r = 1. Show your work for computation problems.

Grade 9·22 problems·~45 min·Common Core Math - HS Algebra·standard·hsa-sse-b-4

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Fluency Practice

For the geometric series with $a = 4$ , $r = \frac{1}{2}$ , $n = 8$ , which formula form is most convenient to use?

$S = \dfrac{a(r^n - 1)}{r - 1}$ , since $r < 1$ .

$S = \dfrac{a(1 - r^n)}{1 - r}$ , since $r < 1$ .

$S = na$ , since $r = 1$ .

Either form gives the same result, and both are equally convenient.