Question

The first and the third terms of an arithmetic progression are equal, respectively, to the first and the third term of a geometric progression and the second term of the arithmetic progression exceeds the second term of the geometric progression by 0.25. Calculate the sum of the first five terms of the arithmetic progression if its first term is equal to 2.

• A. 2.25 or 25
• B. 2.5
• C. 1.5
• D. 3.25

Answer 1

The correct option is B 2.5

Solve this question using options. The average of the sum of the first 5 terms of the AP can be used to get the value of the third term of the AP. If we try to use the options, in option 2, if the sum of the first 5 terms is 2.5, the third term must be $\frac{2.5}{5}=0.5$. This means our AP is 2, 1.25, 0.5, -0.25, -1. The corresponding GP with the same 1st and 3rd terms is 2, 1, 0.5, 0.25 .... The condition for the second term is also matched here.