Question

If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is 

Options

• n(n − 2)

• n(n + 2)

• n(n + 1)

•  n(n − 1)

Answer 1

Here, we are given an A.P. whose n^th term is given by the following expression, `a_n = 2n + 1`. We need to find the sum of first n 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 = 2 ( 1) + 1

   = 2 + 1

   = 3 

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

l = a_n = 2n + 1

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

`S_n = (n /2) [(3) + 2n + 1]`

       `= ( n/2) [ 4 + 2n]`

      `= ( n/2) (2) (2 + n) `

      = n ( 2 + n) 

Therefore, the sum of the n terms of the given A.P. is `S_n = n (2 + n)` .