TS EAMCET · Maths · Sequences and Series
\(1+(1+3)+(1+3+5)+(1+3+5+7)+\ldots\) to 10 terms \(=\)
- A \(385\)
- B \(285\)
- C \(506\)
- D \(406\)
Answer & Solution
Correct Answer
(A) \(385\)
Step-by-step Solution
Detailed explanation
\(T_k = 1+3+\ldots+(2k-1) = k^2\) \(\sum_{k=1}^{10} k^2 = \frac{10(10+1)(2 \cdot 10+1)}{6}\) \(= \frac{10 \cdot 11 \cdot 21}{6} = 5 \cdot 11 \cdot 7 = 385\)
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