Question

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

Answer 1

In the given problem, let us take the first term as a and the common difference d

Here, we are given that,

Also, we know,

For the 5^th term (n = 5),

Similarly, for the 12^th term (n = 12),

Subtracting (3) from (4), we get,

Now, to find a, we substitute the value of d in (4),

So, for the given A.P

So, to find the sum of first 20 terms of this A.P., we use the following formula for the sum of n terms of an A.P.,

Where; a = first term for the given A.P.

d = common difference of the given A.P.

n = number of terms

So, using the formula for n = 20, we get,

Therefore, the sum of first 20 terms for the given A.P. is.