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Mathematics

Can 2n2 - 7 be the nth term of an A.P. Explain.

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Answer

Given,

an = 2n2 - 7

a1 = 2(1)2 - 7 = 2 - 7 = -5

a2 = 2(2)2 - 7 = 8 - 7 = 1

a3 = 2(3)2 - 7 = 18 - 7 = 11

Here, a2 - a1 = 1 - (-5) = 6 and a3 - a2 = 11 - 1 = 10.

Since, difference is not common.

Hence, 2n2 - 7 cannot be the nth term of an A.P.

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