Q1 of 104 Page 491

If the 5^th term of a GP is 2, find the product of its first nine terms.

Given: 5^th term of a GP is 2.

To find: the product of its first nine terms.

First term is denoted by a, the common ratio is denote by r.

∴ ar⁴ = 2

We have to find the value of: a × ar¹ × ar² × ar³ × … × ar⁸

= a⁹r^{1 + 2 + 3 + 4 + … + 8}

= a⁹r³⁶

= (ar⁴)⁹

= (2)⁹

= 512

Ans:512.

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If the 5th term of a GP is 2, find the product of its first nine terms.