Question

The fourth term of an A. P is equal to 3 times the first and the seventh term exeeds twice third term by 1. Find the first term and comman difference.

Answer 1

Hi ,

Let a and d are first term and common

difference of an A.P

nth term = an = a + ( n - 1 )d

fourth term = a4 = a + 3d

first term = a1 = a

seventh term = a7 = a + 6d

third term = a3 = a + 2d

according to the problem given ,

a4 = 3a1

a + 3d = 3a

3d = 3a - a

3d = 2a

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

a7 - 2a3 = 1

a + 6d - 2 ( a + 2d ) = 1

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

- a + 2d = 1--- ( 2 )

substitute ( 1 ) in equation ( 2 ), we get

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

- a + 4a / 3 = 1

( -3a + 4a ) / 3 = 1

a / 3 = 1

a = 3

put a = 3 in equation ( 1 ) , we get

d = ( 2 × 3 ) / 3

d = 2

Therefore ,

first term = a = 3

common difference = d = 2

I hope this helps you.

:)