Question

In an AP the sum of first n terms is 3n square/2 + 13/2*n find its 25th term.

Answer 1

n term sum = 3n²/2 + 13n/2
as we know that nth term = (Sum of nth term ) -( sum of (n-1)th term)
method 1
so 25th term = (sum of 25 terms) - ( sum of 24 terms)
                     =(3×(25)²/2 +(13×25)/2) - ( 3×(24)²/2 + (13×24)/2)
                     = 1100 - 1020
                     = 80
method 2
1st term = 8
sum of 2 terms = 19
2nd term = 19 - 8= 11
so. difference = 11- 8 = 3
25th term = (8 + (25 -1)×3) = 80