The 3rd term of an AP is 24 and the 5th term is 36. What is the sum of the first 20 terms?

Let a1, a2, a3, a4, a5, ..., a20 are terms of an
A.P

Given that:

a3 =
24

a5 36

We need to find the
sum of the first 20 terms.

First we need to find the value
of a1 and the common difference r.

We know
that:

a3= a1+ 2r = 24
.............(1)

a5= a1+ 4r = 36
..............(2)

We will subtract (1) from (2)
.

==>  2r = 12 ==> r= 6  ==> a1= 24-
12 = 12

Now we know that the sum of n terms of A.P is given
by :

Sn = (n/2)*(2a1+ (n-1)*r
)

==> S20 = (20/2) ( 2*12 + 19*6) = 10* 138 =
1380.

Then the sum of the first 20 terms is
1380.