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

Hey mate !


There is an AP, The 4th term is three times the first. So the relation is

3a = a + 3d, or

2a = 3d, or

a = (3/2)d …(1)

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

a+6d = 2(a+2d)+1, or

a + 6d = 2a+4d+1, or

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

a = 2d-1 …(2). Equate (1) and (2)

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

3d = 4d-2, or

4d-3d=2, or d = 2 and a = 3.

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


_______________________


Thanks !