Middle term?

Algebra Level 1

If the sum of three consecutive terms in a geometric progression is 21 and their product is 216, then which of the following is the middle term of the given geometric progression?

12 3 8 6

Ojasee Duble by Ojasee Duble , 19, India

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2 solutions

Jun Arro Estrella
Nov 10, 2017

Actually you only need the information on the product.

x, y, z

y² = xz

xyz = 216

y²y = y³ = 216

y = 6

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Wow! That's a quick solution! Thanks :)

Ojasee Duble - 3 years, 7 months ago

So, a + ar + ar^2 = 21 and ax(ar)x(ar^2) = 216. Solve this system we have a = 3 and r = 2. Therefore the middle term is axr and 3x2 = 6.

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