Question

The sum of first five terms of an A.Pis 45 and that of it's first 15 terms is 435 find the sum of n terms of this A.P

Answer 1

let the first five terms of this AP be 
a-2d. a-d, a, a+d, a+2d

Adding them we get 5a = 45
Therefore a=9.

sum of fifteen terms would be 

$\frac{15}{2} (2*(9-2d) + (15-1)d) = 435$

Solving this we get d and thus a.
putting it in the general formula we get the sum to n terms of this AP.