Question

Find the sum of n terms of an A.P. whose nth terms is given by a_n = 5 − 6n.

Answer 1

Here, we are given an A.P., whose n^th term is given by the following expression, 

`a_n = 5   -6n`

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 = 1in the given equation for n^th term of A.P.

a = 5 - 6(1)

= 5 - 6

= -1

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

`a_n = 5 - 6n`

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

`S_n = (n/2) [(-1) + 5 - 6n]`

`= (n/2) [4 - 6n]`

`= (n/2) (2)[2 - 3n]`

= (n)(2 - 3n)

Therefore the sum of the n terms of the given A.P. is  `(n)(2 - 3n)`