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Mathematics

If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.

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Answer

Let first term of the G.P. be a and it's common ratio be r.

Given,

⇒ a = 2

⇒ a3 = 8

⇒ ar2 = 8

⇒ 2r2 = 8

⇒ r2 = 4

⇒ r =√4 = ±2

a2 = ar

Let r = -2

⇒ a2 = 2(-2) = -4

Let r = 2

⇒ a2 = 2(2) = 4.

Hence, a2 = 4 or -4.

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