JEE Mains · Maths · STD 11 - 8. sequence and series
If the sum of an infinite \(GP\) \(a, ar, ar^{2}, a r^{3}, \ldots\) is \(15\) and the sum of the squares of its each term is \(150 ,\) then the sum of \(\mathrm{ar}^{2}, \mathrm{ar}^{4}, \mathrm{ar}^{6}, \ldots\) is :
- A \(\frac{5}{2}\)
- B \(\frac{1}{2}\)
- C \(\frac{25}{2}\)
- D \(\frac{9}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Sum of infinite terms : \(\frac{\mathrm{a}}{1-\mathrm{r}}=15....(i)\) Series formed by square of terms: \(\mathrm{a}^{2}, \mathrm{a}^{2} \mathrm{r}^{2}, \mathrm{a}^{2} \mathrm{r}^{4}, \mathrm{a}^{2} r^{6} \ldots \ldots\)…
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