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The fourth term of a geometric sequence is 2 and the sixth term is 8....

Further Mathematics
WAEC 2011

The fourth term of a geometric sequence is 2 and the sixth term is 8. Find the common ratio.

  • A. \(\pm 1\)
  • B. \(\pm 2\)
  • C. \(\pm 3\)
  • D. \(\pm 4\)
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Correct Answer: Option B
Explanation

\(T_{n} = ar^{n - 1}\) (Exponential sequence)

\(T_{4} = ar^{3} = 2 .... (1)\)

\(T_{6} = ar^{5} = 8 ......(2)\)

Divide (2) by (1),

\(\frac{ar^{5}}{ar^{3}} = \frac{8}{2} \)

\(r^{2} = 4\)

\(r = \pm 2\)


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