Question

Find the sum of the first 15 terms of each of the following sequences having the nth term as

y_n = 9 − 5n

Answer 1

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

y_n = 9 − 5n. 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 the n^th term of A.P.

y = 9 - 5(1)

= 9 - 5

= 4

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

`l = a_n = 9 - 5n`

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

`S_15 = (15/2) [(4) + 9 - 5(15)]`

`= (15/2)[13 - 75]`

= (15/2)(-62)

= (15)(-31)

= -465

Therefore, the sum of the 15 terms of the given A.P. is `S_15 = -465`