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The third term of a GP is 4; Find the product of its five terms.

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Given that the third term of the GP, a3 = 4 

Let us assume the GP mentioned in the question be,

\(\frac{A}{R^3},\)With the first term \(\frac{A}{R}\), A, AR, AR ......

With the first term \(\frac{A}{R^2}\) and common ratio R.

Now, the third term in the assumed GP is A. 

So, A = 4 (given data) 

Now,

Product of the first five terms of GP = \(\frac{A}{R^2}\) \(\times\) \(\frac{A}{R}\) \(\times\) A \(\times\) AR \(\times\) AR2 = A5

So, the required product = A5 = 45 = 1024

∴ The product of first five terms of a GP with its third term 4 is 1024.

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