COMEDK · Maths · 5. Sequences and Series

If the sum of 12 th and 22 nd terms of an AP is 100 , then the sum of the first 33 terms of an \(\mathrm{AP}\) is

A 1700
B 1650
C 3300
D 3500

Verified Solution

Answer & Solution

Correct Answer

(B) 1650

Step-by-step Solution

Detailed explanation

Here, \(T_{12}=a+11 d\) and \(T_{22}=a+21 d\) Since, \(100=T_{12}+T_{22}\) \(\begin{aligned} & \therefore \quad 100=a+11 d+a+21 d \\ & \Rightarrow a+16 d=50 \quad \ldots(\mathrm{i}) \end{aligned}\) Now,…

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.

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