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Mathematics — CBSE Class 10 board question

Q1. [1]
The next (4th) term of the A.P. $\sqrt{18}$, $\sqrt{50}$, $\sqrt{98}$, … is :
  1. A $128$
  2. B $140$
  3. C $162$
  4. D $200$
Previously asked in CBSE board exam
2024 30/5/1 Q1
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer

The terms simplify: $\sqrt{18}=3\sqrt{2}$, $\sqrt{50}=5\sqrt{2}$, $\sqrt{98}=7\sqrt{2}$, so $d=2\sqrt{2}$. The 4th term $=7\sqrt{2}+2\sqrt{2}=9\sqrt{2}=\sqrt{162}$. Answer: (C) $\sqrt{162}$

Explanation

Rewrite each term as a multiple of $\sqrt{2}$: the AP is $3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, \ldots$ with common difference $2\sqrt{2}$. The 4th term is $9\sqrt{2} = \sqrt{81 \times 2} = \sqrt{162}$. Note the options are under the square root — don't forget to square back when matching the answer.

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