Question

The number of terms of an AP is even. The sum of the odd terms is 24 and of the even terms is 30. The last term exceeds the first by 1012. Then the number of terms in the series is ______.

Answer 1

Explanation:
Let the total number of terms be 2n, and the first term is a and common difference be d.
a+(2n-1)d=1 .........(1)1-a=10.5
If we take odd terms only it will also be an A.P. of n terms with a common difference of 2d.
24=n/2{2a+(n-1)2d}24=n(a+(n-1)d).....(2)
30=n/2{2(a+d)+(n-1)2d}30=n(a+nd).....(3)
Put the value of equation (3) in equation (2)
24=30-ndnd=6,
[Putting in equation (1)]
12-d=10.5d=1.5
So, n=4a=1.5
So no. of terms 8.
Series 1.5,3,4.5,6,7.5,9,10.5,12
Hence, the correct answer is 8.