Find the sum of the first 15 terms of each of the following sequences having nth term as xn = 6 − n .
Here, we are given an A.P. whose nth term is given by the following expression, xn = 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 nth term of A.P.
x = 6 -1
Now, the last term (l) or the nth term is given
l = an = 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) `
= - 30
Therefore, the sum of the 15 terms of the given A.P. is S15 = - 30.