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.