Question

The sum of the 2nd term and the 7th term of an A.P is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P

Answer 1

The general term of an AP is given by `t_n = a + (n - 1)d`

Now `t_2 + t_7 = 30`

=> (a + d) + (a + 6d) = 30

=> 2a + 7d = 30 ...(i)

Next `2 xx t_8 - t_15= 1`

`=> 2 xx (a + 7d) - (a + 14d) = 1`

=> 2a + 14d -  a - 14d = 1

=> a =  1

Substituting the value of a in (i) we get

`2 xx  1+ 7d = 30`

=> 7d = 28

`=> d = 4`

Thus required A.P = a, a + d, a + 2d, a + 3d

= 1, 5, 9, 13, ....