Find the sum of the first 15 terms of each of the following sequences having nth term as *x*_{n} = 6 − *n .*

#### Solution

Here, we are given an A.P. whose *n*^{th} term is given by the following expression, x_{n} = 6 - n . We need to find the sum of first 15 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.

x = 6 -1

= 5

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

l = a_{n} = 6 - n

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

`S_15 = (15/2) [(5) + 6 - 15]`

`= (15/2) [11-15]`

`=(15/2) (-4) `

= (15)(-2)

= - 30

Therefore, the sum of the 15 terms of the given A.P. is **S _{15} = - 30.**