What is the sum of the terms in a sequence of consecutive multiples of 3? (1) There is an odd number of terms in the sequence. (2) The average of the sequence is zero.
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I initially thought (1) might be sufficient, but then realized we don't know the actual terms. For example, the sequence could be 3,6,9 (sum 18) or -3,0,3 (sum 0), both have odd number of terms. So (1) alone doesn't give a unique sum. (2) alone says average is zero, so sum = 0 regardless of number of terms. So (2) is sufficient. Thus answer is B.
Yes, exactly! The average of any set of numbers is sum divided by count. If average is zero, sum must be zero. So (2) alone is enough.
I fell for the trap too. But wait, does the sequence have to be non-empty? The question says 'a sequence of consecutive multiples of 3', so presumably it has at least one term. If it had zero terms, average undefined, but that's not typical.
Is statement (1) completely useless? It seems like it's there to trick you into thinking about symmetry. But as shown, odd number of terms doesn't guarantee average zero unless the middle term is zero. So yeah, (1) alone is not sufficient.
Yep, classic distractor. I've seen similar problems where they try to make you think odd number implies something about the sum, but it doesn't.
This one was pretty straightforward for me. The key is to translate the question: sum = average * number of terms. Statement (2) directly gives average = 0, so sum = 0. Statement (1) gives no info about sum. So B. I think this is around 500 level.
I have a question: If the sequence has an odd number of terms and average zero, then the middle term must be zero. But that's not needed. The answer is B, right?
Yes, B. You don't even need to consider both statements together. (2) alone is sufficient.
What it tests
Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.
Common trap
Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.