Question
If n is a positive integer, what is the smallest value of n such that
(n+10) + (n+11) + (n+12) + ......+ (n+58) is a perfect square?
(n+10) + (n+11) + (n+12) + ......+ (n+58) is a perfect square?
Answer: Option A
:
A
This is an arithmetic sequence with 49 terms, and middle term (n + 34), so the sum is equal to 49(n + 34). Since 49 is 72, which is already a perfect square, we need the smallest value of n such that (n + 34) is a perfect square. We see that for n=2, n+34 is a perfect square (since 36=62).
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:
A
This is an arithmetic sequence with 49 terms, and middle term (n + 34), so the sum is equal to 49(n + 34). Since 49 is 72, which is already a perfect square, we need the smallest value of n such that (n + 34) is a perfect square. We see that for n=2, n+34 is a perfect square (since 36=62).
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