Question

Find the sum of the first 25 terms of an A.P. whose nth term is given by a_n = 7 − 3n

Answer 1

Here, we are given an A.P. whose n^th term is given by the following expression,  `a_n = 7 - 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 n^th term of A.P.

a = 7 - 3(1)

= 7 - 3

= 4

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

`l = a_n = 7 - 3n`

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

`S_25= (258/2)[(4) + 7 - 3 (25)]`

`= (25/2) [11 - 75]`

`= (25/2) (-64)`

= (25)(-32)

= -800

Therefore, the sum of the 25 terms of the given A.P. is `S_n = -800`