Question

If fourth therm of an $A.P$ is thrice its first term and seventh term is one less than the twice of third term, then its common difference is ?

• A. $1$
• B. $2$
• C. $-2$
• D. $3$

Answer 1

The correct option is B $2$

Let a be the first term and d be the common difference.

The 4th term can be written as ‘a+3d’ and 7th term can be written as ‘a+6d’.

As per the question,

1. a+3d = 3a → 2a-3d=0

2. a+6d=2(a+2d)+1 →a+6d=2a+4d+1 →a-2d+1=0

Now solve the 2 quations, you will get:

d=2 & a=3

Hence, the first term is 3 and the common difference is 2.

The AP would be,

3,5,7,9,11,…..