Discussion

Explanation:

Let the first term be ‘a’ and common ratio be ‘r’.

∴ The three terms in GP are a, ar, ar².

Also given, a, 3ar and ar² are in Arithmetic Progression.

∴ a + ar² = 2 × 3ar

⇒ r² – 6r + 1 = 0

⇒ r = $\frac{6\pm \sqrt{6^2-4\times 1\times 1}}{2}$ = 3 ± 2√2

Since the terms are in an increasing geometric progression hence r should be greater than 1.

⇒ r = 3 + 2√2

Hence, option (b).

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