माना \(x _1, X _2, x _3, \ldots, x _{20}\) एक गुणोत्तर श्रेढ़ी में हैं, जिसमें \(x _1=3\) तथा सार्व अनुपात \(\frac{1}{2}\) है। प्रत्येक \(x _{ i }\) की जगह \(\left( x _{ i }- i \right)^2\) लेकर नये आंकड़ें बनाए जाते हैं। यदि नये आंकड़ों का माध्य \(\overline{ x }\) है तो महत्तम पूर्णाक \(\leq \overline{ x }\) है \(..........\) I

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.