Question

The common difference of an A.P. \(\sqrt{18},\,\sqrt{50},\,\sqrt{98},\,\sqrt{162},\,\ldots\) is

• A. \(2\)
• B. \(2\sqrt{2}\)
• C. \(3\)
• D. \(2\sqrt{3}\)

Hint:

Always try to simplify square roots to find patterns in A.P. sequences.

Answer 1

The Correct Option is B

Step 1: Simplify radicals.
\(\sqrt{18}=3\sqrt{2},\;\sqrt{50}=5\sqrt{2},\;\sqrt{98}=7\sqrt{2},\;\sqrt{162}=9\sqrt{2}\).
Step 2: Check differences.
\(5\sqrt{2}-3\sqrt{2}=2\sqrt{2},\;7\sqrt{2}-5\sqrt{2}=2\sqrt{2}\). Constant difference.
Thus, \(d=2\sqrt{2}\).