If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of the first 20 terms?

assuming an AP whose first term is a and the common difference is d

To find: the sum of the first 20 terms

Given 5^th term is 30

So, a + 4d = 30...(i)

Given 12^th term is 65

So, a + 11d = 65…(ii)

Solving (i) and (ii) we get

a = 10 and d = 5

we know that the sum of AP is given by the formula:

substituting the values in the above equation

s = 1150