Consider a series of numbers, $S_1$ , $S_2$ , $S_3$ , ..., defined by the formula $S_k = k^2 - k$ for every positive integer k. If $S_n$ equals 72, what is the value of $S_{n - 1}$ ?

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132

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Explanation

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Official Explanation

Official

The sequence is defined by

S_k = k^2 - k

. Given that

S_n = n^2 - n = 72

, we can rearrange this to

n(n - 1) = 72

. Solving for n, we…

Comments

SohiniAug 13, 2024

thanks

PrajwalMar 13, 2025

appreciated!

What this question tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.