alleryHow many terms of the AP 1, 4, 7, ... sum to 287?
A16
B12
C15
D14
Answer & Solution
Correct answer: D. 14
1. a = 1, d = 3 and S_n = n/2 * (2 + 3(n - 1)) = n(3n - 1)/2.
2. Set n(3n - 1)/2 = 287, so 3 n^2 - n - 574 = 0.
3. Factor: (3n + 41)(n - 14) = 0.
4. Take positive n = 14.
_Source: Selina Concise Mathematics Class 10, Ch on Arithmetic Progression (Mistral OCR'd PDF), section on sum_
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