1st term of an A.P. of consecutive integers is n2 + 1 (n is a positiv

1.	1st term of an A.P. of consecutive integers is n2 + 1 (n is a positive integer). Sum of 1st 2n terms of the series will be. (a) n( 2n2 + 2n + 1) (b) (2n2 + 2n + 3) (c) n(2n2 + 2n + 3) (d) None of these.
Answer» Correct option (a) n( 2n² + 2n + 1) Explanation: S = n² + 1 + n² + 2 +… + n² + 2n = 2n³ + n(2n + 1) = n(2n² + 2n + 1) Alternative Method: Suppose n = 2 then 1^st term of the series will be 22 + 1 = 5. Now we want to find the sum of first 2n = 4 terms. First 4 terms of the series will be 5, 6, 7, 8. Sum = 26. If we put n = 2 in the above options then only option (a) satisfies.

1st term of an A.P. of consecutive integers is n2 + 1 (n is a positive integer). Sum of 1st 2n terms of the series will be. (a) n( 2n2 + 2n + 1) (b) (2n2 + 2n + 3) (c) n(2n2 + 2n + 3) (d) None of these.

Answer»

Correct option (a) n( 2n² + 2n + 1)

Explanation:

S = n² + 1 + n² + 2 +… + n² + 2n = 2n³ + n(2n + 1) = n(2n² + 2n + 1)

Alternative Method: Suppose n = 2 then 1^st term of the series will be 22 + 1 = 5. Now we want to find the sum of first 2n = 4 terms. First 4 terms of the series will be 5, 6, 7, 8. Sum = 26. If we put n = 2 in the above options then only option (a) satisfies.

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1st term of an A.P. of consecutive integers is n2 + 1 (n is a positive integer). Sum of 1st 2n terms of the series will be. (a) n( 2n2 + 2n + 1) (b) (2n2 + 2n + 3) (c) n(2n2 + 2n + 3) (d) None of these.

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