# It is given that the sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is 40 and the common difference is 6. We have to find n.

Sir please give me a detailed solution of this question as it is very important for examination and it is from ML AGGARWAL ( avichal publication) Arithmetic Progression Chapter 9 question no 14

## Let Sn be the sum of n terms of an AP with first term a=8 and common difference d=20. Then,

Sn=2n(2a+(n−1)d)

## ⇒Sn=2n(2×8+(n−1)×20)

## ⇒Sn=2n(16+20n−20)

⇒Sn=2n(20n−4) …1

similarly Let S2n be the sum of 2n terms of an AP with first term a1=30 and common difference d1=8. Then,

S2n=22n(2a1+(2n−1)d1)

## ⇒S2n=22n(2×30+(n−1)×8)

## ⇒S2n=22n(60+8n−8)

⇒S2n=n(8n+52) …2

According to question Sn=S2n

2n(20n−4)=n(8n+52)

⇒10n−2=8n+52

⇒2n=54

⇒n=27