UPSC NDA Math Model Paper 2

It is given that first term a = 3. Let the common difference be d.
Also, the sum of the first 8 terms is twice the sum of the first 5 terms
⇒S8=2S5
⇒

8

2

[3+{3+(8−1)d}] =2×

5

2

[3+{3+(5−1)d}]
⇒4(6+7d)=5(6+4d)
⇒24+28d=30+20d
⇒8d=6
⇒d=

3

4

.
∴ The common difference of the given arithmetic progression is

3

4

.