Problem: Let s1 be the sum of the first n terms of the arithmetic sequence 8,12,⋯ and let s2 be the sum of the first n terms of the arithmetic sequence 17,19,⋯. Then s1=s2 for:
Answer Choices:
A. no value of n
B. one value of n
C. two values of n
D. four values of n
E. a value of n greater than four
Solution:
s1=2n(16+(n−1)4),s2=2n(34+(n−1)2). But s1=s2 implies 2n(12+4n)=2n(32+2n)
∴12+4n=32+2n,n=10 so that choice ( B ) is correct.