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

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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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