Mathematics

Find the next term of the list of numbers $\dfrac{1}{6}, \dfrac{1}{3}, \dfrac{2}{3}, …$

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The given list of numbers $\dfrac{1}{6}, \dfrac{1}{3}, \dfrac{2}{3}, …$ is a G.P. with first term a = $\dfrac{1}{6}$ and common ratio = r = 2.

By formula, a_n = ar^{n - 1}

∴ a₄ = $\dfrac{1}{6}(2)^3 = \dfrac{8}{6} = \dfrac{4}{3}.$

Hence, the next term of the G.P. is $\dfrac{4}{3}$ .

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