The sum of 15 consecutive multiples of 7 is 1,470. What is the sixth smallest of these multiples?

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Comments

AmelAug 29

Wait, is there a faster way than listing all 15 terms? I used a + (n-1)d but got tangled up.

JasonSep 6

For consecutive multiples, the average of the terms equals the middle term. 1470/15 = 98, that's your 8th term.

RaghavSep 8

Then just walk back two steps of 7 to get the 6th. Much cleaner.

PhillipAug 1

Got 77 but I had to double check I wasn't off by one. Sixth smallest vs sixth from the middle trips me up.

AdrielAug 3

Same, I initially found the 7th term by accident. Careful with the counting.

ScottJul 26

Thanks, the average = middle term trick is gold for any evenly spaced set.

HannahJul 12

This one felt fair for 555-605. Took me about 90 seconds once I saw the average shortcut.

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.