Question

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

`a_n = 3 + 4n`

Answer 1

Here, we are given an A.P. whose n^th term is given by the following expression `a_n = 3 + 4n`. 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.

a= 3 + 4(1)

= 3 + 4

= 7

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

`l = a_n = 3 +4n`

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) + 3 + 4 (15)]`

`= (15/2)[10 + 60]`

= (15/2)(70)

`= (15)(35)`

= 525

Therefore, the sum of the 15 terms of the given A.P. is `S_15 = 525`