Back to Derive geometric series formula — Problem 3 · Task Set 7

HSA.SSE.B.4 Tutor Intake — Geometric Series Formula

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Grade 9·10 problems·~15 min·Common Core Math - HS Algebra·standard·hsa-sse-b-4

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Concepts

A student wants to find the sum of $7 + 7 + 7 + 7 + 7$ (five 7s).
They try to apply the formula $S = \dfrac{a(1-r^n)}{1-r}$ with
$a = 7$ , $r = 1$ , $n = 5$ .

What should the student do instead, and why?

Use $S = na = 5 \times 7 = 35$ , because the formula is undefined when $r = 1$ (divides by zero)

Substitute $r = 1$ into the formula to get $S = 7(1-1)/0 = 0$

Use $S = ar^n = 7 \times 1^5 = 7$

The formula works fine; the answer is $5 \times 7 = 35$ using the formula