If the terms of a sequence are $t_1, t_2, t_3, ..., t_n$ , what is the value of $n$ ? (1) The sum of the $n$ terms is 3,124. (2) The average (arithmetic mean) of the $n$ terms is 4.

Answer Choices

Correct answer marked below

Statement (1) ALONE is sufficient

Statement (2) ALONE is sufficient

BOTH statements TOGETHER are sufficient

Correct

EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient

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Comments

AustinSep 19

Wait, is this really only 505-555? I stared at it way too long before realizing neither statement gives me the actual terms. Classic DS trap.

SandraSep 25

Same here. I kept trying to build a sequence that sums to 3,124.

JasleenSep 27

Something feels off — statement (1) says the sum is 3,124, but statement (2) says the mean is 4. If both were true at once, n would have to be 781. Since that's a whole number, doesn't that mean together they work?

Sri1d ago

That's exactly the kind of thing the test wants you to check. Does a valid sequence with that n actually exist?

Mannanjust now

Right, the statements don't have to be consistent with each other in DS.

MalayAug 25

Quick note: this is testing whether you notice that n shows up in the sum but the sum alone doesn't pin it down. Average alone definitely doesn't. Took me a second to see it.

What this question tests

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.

If the terms of a sequence are t1,t2,t3,...,tnt_1, t_2, t_3, ..., t_nt1​,t2​,t3​,...,tn​, what is the value of nnn? (1) The sum of the nnn terms is 3,124. (2) The average (arithmetic mean) of the nnn terms is 4.