Problem: Let S be the sum of the first nine terms of the sequence, x+a,x2+2a,x3+3a,…. Then S equals:
Answer Choices:
A. x+150a+x+x8​
B. 50a−x−1x+x10​
C. x+1x9−1​+45a
D. x−1x10−x​+45a
E. x−1x11−x​+45a
Solution:
x+x2+x3+…+x9
S1​=1−xx(1−x9)​=x−1x10−x​
a+2a+3a+…+9a
S2​=29​(a+9a)=45aS=S1​+S2​