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  • Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5 . Let the sum of its first five terms be <img alt="\frac{98}{25}" src="/latex-image/?%5Cfrac%7B98%7D%7B25%7D"

Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5 . Let the sum of its first five terms be \frac{98}{25}. Then the sum of the first 21 terms of an AP, whose first term is \mathrm{10 a r, n^{\text {th }}} term is \mathrm{a_{n}} and the common difference is \mathrm{10 a^{2}}, is equal to :
 

Option: 1

21 \mathrm{a}_{11}


Option: 2

22 \mathrm{a}_{11}


Option: 3

15 \mathrm{a}_{16}


Option: 4

14 \mathrm{a}_{16}


Answers (1)

best_answer

 

\begin{aligned} &\text { Sum of 21 terms } \\ &\mathrm{=\frac{21}{2}\left[2(10 a r)+20 \cdot \text { loar }^{2}\right] }\\ & \mathrm{=21 r\left(10 a r+1.00 a^{2}\right) }\\ & \mathrm{=21\left[a_{1}+(11-1) \cdot 10 a^{2}\right)} \\ & \mathrm{=21\left(a_{1}+(11-1) d\right) }\\ &\mathrm{=21 \cdot a_{11}} \\ &\therefore \text { option (A) } \end{aligned}

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Rakesh

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