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2014-08-17T23:21:49+08:00

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55 consecutive numbers. (from 10 to 65)
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2014-08-18T00:48:26+08:00

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S_n= \frac{n}{2}[(2a_1+(n-1)d]

n = ?                    (number of terms)
a_1 = 10         (the first term)
S_n = 2035     (their sum)
d = 1        (common difference of 1 since they are 'consecutive' integers)

2035= \frac{n}{2}[(2(10)+(n-1)1] \\  \\ 4070= n[20+n-1] \\  \\ 4070=n[19+n] \\  \\ 4070=19n+n^2 \\  \\ n^2+19n-4070= 0 \\  \\ (n+74)(n-55)=0 \\  \\ n=-74\  ;\ \boxed{n=55}
2 5 2