In an arithmetic progression the 3rd term is 28 and the sum of the first 21 terms is 1932. Find the sum of the first 11 terms.
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Got 594 but it took me way too long. Setting up a + 2d = 28 and the 21-term sum equation, then solving for d... I kept second-guessing my d value because it wasn't a clean integer. Anyone else find the arithmetic annoying here?
Yes! The d value tripped me up too. I redid the division like three times.
Honestly the setup is the hard part, the rest is just plugging in.
Is there a shortcut using the average of the AP? Like the sum of first 21 is 21 times the middle (11th) term, since 21 is odd. That gives you the 11th term immediately, and then you can relate it back to the 3rd term. Way faster than writing two full equations.
This is the move. Median term = average for odd number of terms.
Wish I'd seen this before grinding through the algebra.
The distractor choices being 572, 580, 593, 594, 600 is brutal — two of them are within 1 of each other. Definitely a trap for a small arithmetic slip.
Took me a second but I got there. The key is remembering S_n = n/2 * (first + last) works nicely once you know d.
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.