AP EAMCET · Maths · Sequences and Series
The \(n^{\text {th }}\) term of the series \(1+(3+5+7)+(9+11+13+\) \(15+17)+\ldots\)
- A \((2 n+1)\left[n^2-(n-1)^2\right]\)
- B \((2 n-1)\left[(n-1)^2-n^2\right]\)
- C \((2 n+1)\left[(n-1)^2-n^2\right]\)
- D \((2 n-1)\left[(n-1)^2+n^2\right]\)
Answer & Solution
Correct Answer
(D) \((2 n-1)\left[(n-1)^2+n^2\right]\)
Step-by-step Solution
Detailed explanation
Given the series \(\underbrace{1}_{t_1}+\underbrace{(3+5+7)}_{t_2}+\underbrace{(9+11+13+15+17)}_{t_3}+\ldots .\) \(\because\) Number of numbers in \(n^{\text {th }}\) term \(=2 n-1\) Let first term in \(t_{\mathrm{n}}=a_{\mathrm{n}}\) So, \(t_n=\{a, a+2, a+4, \ldots\). upto…
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