Question

The fourth term of an AP is equal to the three times it's seventh term exceeds twice the third term by 1. Find the first term and common difference?

Answer 1

`a = 2/13`
`d = -15/13`

Explanation:

`T_4 = 3 T_7` .........(1)
`T_4 - 2T_3 = 1` ........(2)

`T_n = a + (n-1)d`
`T_4 = a + 3d`
`T_7 = a + 6d`
`T_3 = a + 2d`

Substituting values in the (1) equation,
`a + 3d = 3a + 18d`
`= 2a + 15d = 0` ..............(3)

Substituting values in the (2) equation,
`a + 3d - (2a + 4d) = 1`
`= a + 3d - 2a - 4d = 1`
`-a -d = 1`
`a + d = -1` ............(4)

On solving equations (3) and (4) simultaneously we get,
`d = 2/13`
`a = -15/13`