MHT CET · Maths · Sequences and Series

The sum to 10 terms of the series $1 \times 3^{2}+2 \times 5^{2}+3 \times 7^{2}+\ldots \ldots \ldots \ldots . .$ is

A 13,495
B $15,595$
C $13,000$
D 13,695

Verified Solution

Answer & Solution

Correct Answer

(D) 13,695

Step-by-step Solution

Detailed explanation

$1 \times 3^{2}+2 \times 5^{2}+3 \times 7^{2}+$
Term : $\rightarrow 2(2 q+1)^{2}$
$S=\sum_{\varepsilon=1}^{10} z(2 q+1)^{2}$
$S=\sum_{\varepsilon=1}^{10}\left(4 z^{2}+4 z+1\right) \varepsilon$
$S=\sum_{z=1}^{10}\left[4 z^{3}+4 z^{2}+2\right]$
$S=\frac{4 \times 10^{2} \times 11^{2}}{4}+\frac{4 \times 10 \times 11 x}{6}$$+\frac{10 \times 11}{2}$
$S=13,695$

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.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app

The sum to 10 terms of the series \(1 \times 3^{2}+2 \times 5^{2}+3 \times 7^{2}+\ldots \ldots \ldots \ldots . .\) is

Answer & Solution

Step-by-step Solution

See the Complete Solution