The 3rd and 6th terms of a geometric progression (G.P.) are \(\frac{8}{3}\) and \(\frac{64}{81}\) respectively, find the common ratio.

  • A \(\frac{1}{3}\)
  • B \(\frac{2}{3}\)
  • C \(\frac{3}{4}\)
  • D \(\frac{4}{3}\)
waec 2016furthermathematics

The correct answer is B. \(\frac{2}{3}\)

\(T_{n} = ar^{n-1}\) (for a geometric progression)

\(T_{3} = ar^{3-1} = ar^{2} = \frac{8}{3}\)

\(T_{6} = ar^{6-1} = ar^{5} = \frac{64}{81}\)

Dividing \(T_{6}\) by \(T_{3}\),

\(\frac{ar^{5}}{ar^{2}} = \frac{\frac{64}{81}}{\frac{8}{3}} \implies r^{3} = \frac{8}{27}\)

\(\therefore r = \sqrt[3]{\frac{8}{27}} = \frac{2}{3}\)

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