Question

Sum of the first 14 terms of an A.P. is 1505 and its first term is 10. Find its 25th term.

Answer 1

Sum of n terms = Sn = n/2 [ 2a + (n-1) d ]
where a = first term d = common difference

therefore, S14 = 14/2 [2*10 + (14-1) d ] = 1505

solve for d, we get, 215 = 20 + 13d
hence, d = 15.

now, an = a + (n-1) d
therefore, a25 = 10 + (25-1) 15
a25 = 10 + 24 * 15 = 370.