G.P. is easy

Algebra Level 2

If the fifth term of a geometric progression is 2, what is the product of its first 9 terms?


The answer is 512.

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Vighnesh Raut by Vighnesh Raut , 23, India

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3 solutions

Nicolas Bryenton
Jul 17, 2014

The fifth term will be the geometric mean of the nine terms, that is,

x 9 = 2 \sqrt [ 9 ]{ x } = 2

when x is the product of all nine terms. Raise each side of the equation to the ninth power to find that x = 512 \boxed { x=512 }

2 Helpful 0 Interesting 0 Brilliant 0 Confused

If a is the first term and r is the common ratio then the 5th term is a r^4. The product of the first 9 terms is a^9 * r^36 = (a r^4)^9 = 2^9 = 512.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Yeah, did the same way.

Sudo Jarvis - 5 years, 10 months ago
Rishabh Jain
Jun 22, 2014

the GP is 2,2,2,.....2,2 so product of 9 2's is 512

0 Helpful 0 Interesting 0 Brilliant 0 Confused

This is an example, not a solution. It only shows the product of one of the possible geometric series, of the infinite possibilities. It does not show that the product of all nine terms is a constant.

Nicolas Bryenton - 6 years, 11 months ago

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