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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)
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Solution
Here, we are given an A.P. whose nth 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 nth term of A.P.
a = 2 ( 1) + 1
= 2 + 1
= 3
Now, the last term (l) or the nth term is given
l = an = 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)` .
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