Question

Find the sum of the first 15 terms of each of the following sequences having nth term as  x_n = 6 − n .

Answer 1

 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 S₁₅ = - 30.