Question

The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1.
Find the first term and the common difference.

Answer 1

Answer:

The 4th term is three times the first. So the relation is

2a= 3d

a = (3/2)d …(1)

The 7th term exceeds twice the third term by 1. So the relation is

2a- a= 6d- 4d- 1

a= 2d- 1 …(2)

Equate (1) and (2)

a = (3/2)d = 2d-1

3d= 4d- 2

4d- 3d= 2

d = 2 and a = 3.

The first term is 3 and the common difference is 2.  

The series of the AP is 3, 5, 7, 9, 11, 13, 15...

Step-by-step explanation: