Question

Arithmetic Progression

The sum of the first twelve terms of an AP is three times the sum of the first six terms, then the ratio of the first term to the common difference is

Answer 1

Answer:

Let a be the first term and d be the common diff

S12=(12/2){2a+(12-1)d}=6(2a+11d)

S6=(6/2){2a+(6-1)d}=3(2a+5d)

It is given

6(2a+11d)=3×3(2a+5d)

2(2a+11d)=3(2a+5d)

4a+22d=6a+15d

2a=7d

a/d=7/2