Problem: The number of terms in an A.P. (Arithmetic Progression) is even. The sums of the odd and even numbered terms are 24 and 30 respectively. If the last term exceeds the first by 10.5, the number of terms in the A.P. is
Answer Choices:
A. 20
B. 18
C. 12
D. 10
E. 8
Solution:
Let a,d, and 2n denote the first term, common difference and the even number of terms. If So and Se denote the sums of all odd and all even numbered terms respectively, then
Se=2n[2(n+d)+(n−1)×2d]=30 and
So=2n[3n+(n−1)×2d]=24.
The diftereace Se−S0 equals 2n[2d]=6, nd=6.
∴l−a=a+(2n−1)d−a=10.5 where l denotes the last term.
∴ 2nd −d=10.5,12−d=10.5,d=1.5.∴n=6/d=6/1.5=4,2n=8 or choice (E).