Question

Find the sum of the first 25 terms of an A.P. whose nth term is given by a_n = 2 − 3n.

Answer 1

Here, we are given an A.P. whose n^th term is given by the following expression, `a_n =  2 - 3n`. We need to find the sum of first 25 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 = 2 - 3(1)

= 2 - 3

= -1

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

`l = a_n = 2 - 3n`

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

`S_25 = (25/2)[(-1)+2 -3(25)]`

`= (25/2)[1 - 75]`

`= (25/2)(-74)`

`= (25)(-37)`

= -925

Therefore, the sum of the 25 terms of the given A.P. is `S_25 = -925`