Question

The sum of *_n_* terms of an AP whose first term is 5 and common difference is 36, is equal to the sum of *_2n_* terms of another AP whose first term is 36 and common difference is 5. Find the value of *_n_*

Answer 1

Sum of n terms = n/2(10 + (n-1)36)

= 5n + 18n^2-18n

= 18n^2-13n.

Sum of 2n terms = 2n/2(36+(n-1)5)

= 36n + 5n^2 - 5n

31n +5n^2

Now they are equal.

So, 13n^2 = 44n

n = 44/13