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in Mathematics by (48.4k points)

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.

1 Answer

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Best 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 1st 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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