Question

Six positive numbers are in G.P. such that their product is 1000. If the fourth term is 1, then find the last term.

Answer 1

Let the six numbers in G.P. be \(\frac{a}{r^5}\), \(\frac{a}{r^3}\), \(\frac{a}{r}\), ar, ar³, ar⁵.

Then, Product = 1000

⇒ \(\frac{a}{r^5}\) x \(\frac{a}{r^3}\) x \(\frac{a}{r}\) x ar x ar³ x ar⁵

⇒ a6 = 1000 ⇒ a = \(\sqrt{10}\)

Given, Fourth term = t₄ = ar = 1

⇒ \(\sqrt{10}\) x r = 1 ⇒ \(\frac{1}{\sqrt{10}}\)

∴ Last term = ar⁵ = \(\sqrt{10}\) x\(\bigg(\)\(\frac{1}{\sqrt{10}}\)\(\bigg)\)= \(\frac{1}{100}.\)