The number of terms of an A.P. is even; the sum of the odd term is 24, of the even terms is 30, and the last term exceeds the first by , find the number of terms and the series

let the number of terms be 2n with first term a and common difference d

To find: number of terms and the series

The last term is given as a + (2n - 1) d

It is given that the last term exceeds the first by

So

…(i)

Sum of odd terms is 24

…(ii)

Sum of even terms is 30

…(iii)

Solving (i), (ii) and (iii) we get

d = 1.5

substituting d in (i) we get n = 4

and substituting d and n in (ii) we get a = 1.5

so, the number of terms is 2n = 8, and the sequence is given by a, a + d, a + 2d….

1.5, 3, 4.5, 6, 7.5 , 9, 10.5 , 12