Q. 15.0( 3 Votes )

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

Answer :

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.

∴ ar^{4} = 2

We have to find the value of: a × ar^{1} × ar^{2} × ar^{3} × … × ar^{8}

= a^{9}r^{1 + 2 + 3 + 4 + … + 8}

= a^{9}r^{36}

= (ar^{4})^{9}

= (2)^{9}

= 512

Ans:512.

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