(c) \(\frac{1}{100}.\)
Let the six numbers in G.P. be \(\frac{a}{r^5}\), \(\frac{a}{r^3}\), \(\frac{a}{r}\), ar, ar3, ar5
given, \(\frac{a}{r^5}\) x \(\frac{a}{r^3}\) x \(\frac{a}{r}\) x ar x ar3 x ar5 = 1000
⇒ a6 = 1000 ⇒ a = \(\sqrt{10}\)
Given, T4 = ar = 1 ⇒ \(\sqrt{10}\)r = 1 ⇒ = \(\frac{1}{\sqrt{10}}\)
∴ Last term of G.P. = ar5 = \(\sqrt{10}\) x \(\frac{1}{\sqrt{(10)}^5}\) = \(\frac{1}{100}.\)