Question

The 4th term of an ap is 3 times the first and 7th term exceeds twice the third term by 1 . Find the first term and commmon diffrence

Answer 1

Given

The 4th term of an ap is 3 times the first and 7th term exceeds twice the third term by 1 .

Required

Find the first term and commmon diffrence

3*a = a + 3*d/

2*a = 3*d,  

a = 3/2*d …A)

The seventh term exceeds twice the third term by one. so that,

a+6*d = 2*(a+2*d)+1,  

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

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

a = 2*d-1 …B)

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

3*d = 4*d-2,

4*d-3*d=2,.,

d = 2 and a = 3.

The first term =a= 3 and the common difference =d=  

AP series ==>  3,5,7,9,11,13,15.

The fourth term = 9, that  is 3 *a