Question

Consider a sequence -6, -12, 48, 24, -30, -36, 42, ... continuing in the same style. If the sum of the first n terms of the sequence is 132, what is the value of n?

• A. 11
• B. 13
• C. 18
• D. 24

Hint:

Try extending the sequence and adding it up term by term instead of assuming it behaves like a simple arithmetic progression.

Answer 1

The Correct Option is D

This question asks for a value of n that makes the sum of the first n terms of a signed sequence equal 132. Rather than hunting for a shortcut formula, it is safer to build the sequence out far enough and add it up term by term, then check each of the four given values of n one at a time.

Extending the pattern (the signs run negative, negative, positive, positive, and the size of each term keeps climbing in steps of 6), the sequence out to 24 terms is: -6, -12, 48, 24, -30, -36, 42, 48, -54, -60, 66, 72, -78, -84, 90, 96, -102, -108, 114, 120, -126, -132, 138, 144.

1. n = 11: adding the first 11 terms gives a running total of 30, not 132.
2. n = 13: adding the first 13 terms gives a running total of 24, not 132.
3. n = 18: adding the first 18 terms gives a running total of -84, not 132.
4. n = 24: adding the first 24 terms gives a running total of 174, not 132 either, but this is the closest of the four to 132.

Since none of the four candidate values of n produces a running sum of exactly 132, this question, as given, has no option that is strictly correct. This points to an error in the original question or its answer choices rather than in the method used to solve it.

Let's summarize:

• The running sum after 4, 8, 12, 16 and 20 terms is 54, 78, 102, 126 and 150, and it never equals 132 at any of those checkpoints or at the in-between values asked about.
• Testing every option by direct term-by-term addition, rather than trusting a shortcut formula, confirms none reaches exactly 132.

n = 24 is recorded as the closest available option, though this question should be flagged for review since no listed value of n gives an exact sum of 132.