SAT1000 - P492

Algebra Level 3

Sequence { a n } \{a_n\} is such that a n + 1 + ( − 1 ) n a n = 2 n − 1 a_{n+1}+(-1)^n a_n=2n-1 . Find ∑ k = 1 60 a k \displaystyle \sum_{k=1}^{60} a_k .

Have a look at my problem set: SAT 1000 problems


The answer is 1830.

Alice Smith by Alice Smith , 20, China

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1 solution

a 4 k + 1 + a 4 k + 2 + a 4 k + 3 + a 4 k + 4 = 16 k + 10 ⟹ ∑ k = 1 60 a k = 16 × 14 × 15 2 + 10 × 15 = 1830 a_{4k+1}+a_{4k+2}+a_{4k+3}+a_{4k+4}=16k+10\implies \displaystyle \sum_{k=1}^{60} a_k=\dfrac {16\times 14\times 15}{2}+10\times 15=\boxed {1830} .

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Did it the same way!

Atomsky Jahid - 11 months, 3 weeks ago

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