Question

The 4th term of an ap is three times the first and the 7th term exceeds twice the third term by1. Find the first term and the common difference?

Answer 1

let a1,a2,a3 ,.........,a7 are in a.p. whose common difference is d
a4 = 3a1
a1 + 3d = 3a1
3d = 2a1
a7 = 2a3 + 1
a1 + 6d = 2a1 + 4d + 1
2d = a1 + 1
4a1/3 = a1 + 1
a1 = 3
d = 2

Answer 2

Answer:

d=2

Step-by-step explanation:

a4 = 3a1

a1 + 3d = 3a1

3d = 2a1

a7 = 2a3 + 1

a1 + 6d = 2a1 + 4d + 1

2d = a1 + 1

4a1/3 = a1 + 1

a1 = 3

d = 2