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

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Given: 5th 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 

= a9r1 + 2 + 3 + 4 + … + 8 

= a9r36 

= (ar4)9 

= (2)9 

= 512 .

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