Question

Find the sum of first 20 terms of the sequence whose nth term is `a_n = An + B`

Answer 1

Here, we are given an A.P. whose n^th term is given by the following expression `a_n = An +B`.

We need to find the sum of first 20 terms.

So, here we can find the sum of the n terms of the given A.P., using the formula, 

`S_n = (n/2) (a + l)`

Where a = the first term

l = the last term

So, for the given A.P,

The first term (a) will be calculated using n = 1 in the given equation for the n^th term of A.P.

a = A(1) + B

= A + B

Now, the last term (l) or the n^th term is given

`I = a_n = An + B`

So, on substituting the values in the formula for the sum of n terms of an A.P., we get,

`S_20 = (20/2)[(A + B) + A(20) + B]`

= 10[21A + 2B]

= 210A + 20B

Therefore the sum of the first 20 terms of the given A.P is `S_20 = 210A + 20B`