Question

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

b_n = 5 + 2n

Answer 1

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

We need b_n = 5 + 2n 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 = 1inthe given equation for the n^th term of A.P

b = 5 + 2(1)

=- 5 + 2

= 7

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

`l = b_n = 5 + 2n`

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

`S_15 = (15/2)[(7) + 5 + 2(15)]`

`=(15/2)[12 + 30]`

`= (15/2)(42)`

= (15)(21)

= 315

Therefore, the sum of the 15 terms of the given A.P. is `S_15 = 315`