In a sequence S, each term, after the first term, is obtained by multiplying the previous term by a constant k, where k is an integer other than 1. If the 6th term of the sequence is 243 and the 3rd term is -9, what is the sum of the first five terms of the sequence?

Correct answer marked below

103

101

-59

-61

Correct

-91

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Explanation

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Comments

SuhaniJul 11

Thanks for the clear explanation! I initially got confused with the sign of k, but now it makes sense.

ShubhamJul 21

Same here! I had to remind myself that an odd power of a negative number stays negative.

ReidJun 27

Wait, how did you determine k so quickly? I had to set up the equation and solve for k, but it took me a minute.

GraciousJul 6

I just used the terms given: a6 = a3 * k^3. Since a6 is positive and a3 is negative, k^3 must be negative, so k is negative.

JacopoJul 6

I got k = -3 and then found the first term. The sum came out to one of the answer choices, but I had to be careful with the signs when adding.

SnehamSep 1

This was a solid medium question. The trick is realizing that k is negative because the terms alternate signs.

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.