Problem: Let s1,s2,s3 be the respective sums of n,2n,3n terms of the same arithmetic progression with a as the first term and d as the common difference. Let R=s3−s2−s1. Then R is dependent on:
Answer Choices:
A. a and d
B. d and n
C. a and n
D. a,d, and n
E. neither a nor d nor n
Solution:
s1=2n[2a+(n−1)d],s2=22n[2a+(2n−1)d],
s3=23n[2a+(3n−1)d]
R=s3−s2−s1=2n[6a+9nd−3d−4a−4nd+2d−2a −nd+d]=2n2d, so that (B) is the correct choice.