The 4th term of an AP is thrice the first term and 7th term exceeds twice the 3th term by 1. find the first term and C.D.

Dear Student!

Let *a* and *d* be the first term and common difference of AP respectively.

*n*^{th }term of A.P.,* a _{n}* =

*a*+ (

*n*– 1)

*d*

Given, *a*_{4} = 3*a*

∴ *a *+ (4 – 1)*d* = 3*a*

Given, *a*_{7} = 2 × *a*_{3} + 1

From 1( and (2), we get

When *d *= 2, we get

(Using(1))

Thus, the first term and common difference of A.P. is 3 and 2 respectively.

Cheers!

**
**