Question

There is an arithmetic progression with first term = common difference. The number of terms in this series is 2x. A new series is formed taking the odd terms of the first series upto (2x-1)th term. Find the ratio of the sum of the terms in the old series to that in the new series.

• A.
• B. 1/3
• C.
• D. 2/3

Answer 1

The correct option is C

Option (c)

Let the first term = 1, cd = 1

Take x = 2, 2x = 4, the progression is 1, 2, 3, 4

New progression = 1, 3

Sum to x terms of progression 1 = 1+2+3+4 = 10

Sum to new progression = 4

$Ratio=\frac{10}{4}=\frac{5}{2}$.
Only option c satisfies this condition.