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Arithmetic Series

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March 22, 2006
geometry3D geometryspherearithmetic sequencealgebralinear equation

Problem Statement

Let s1s_1 be the sum of the first nn terms of the arithmetic sequence 8,12,⋯8,12,\cdots and let s2s_2 be the sum of the first nn terms of the arithmetic sequence 17,19⋯17,19\cdots. Assume n≠0n\ne 0. Then s1=s2s_1=s_2 for: (A) no value of n(B) one value of n(C) two values of n\text{(A)} \ \text{no value of n} \qquad \text{(B)} \ \text{one value of n} \qquad \text{(C)} \ \text{two values of n} (D) four values of n(E) more than four values of n\text{(D)} \ \text{four values of n} \qquad \text{(E)} \ \text{more than four values of n}
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