If \(2, (k+1), 8,...\) form an exponential sequence (GP), find the values of k.
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Correct Answer: Option D
Explanation:
Given an exponential sequence, say \(a, b, c,...\), as consecutive terms, then \(\sqrt{a \times c} = b\).
\(\therefore 2, (k+1), 8 \implies \sqrt{2 \times 8} = k + 1\)
\(k + 1 = \pm{4} \implies k = \text{-5 or 3}\)
Given an exponential sequence, say \(a, b, c,...\), as consecutive terms, then \(\sqrt{a \times c} = b\).
\(\therefore 2, (k+1), 8 \implies \sqrt{2 \times 8} = k + 1\)
\(k + 1 = \pm{4} \implies k = \text{-5 or 3}\)