Question

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 \(20\frac{1}{2}\) , find the number of terms and the series.

Answer 1

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 \(20\frac{1}{2}\),

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