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Question: Answered & Verified by Expert
Consider an infinite geometric series with first term $a$ and common ratio $r$. If its sum is 4 and the second term is $\frac{3}{4}$, then:
MathematicsSequences and SeriesBITSATBITSAT 2021
Options:
  • A $a=\frac{4}{7}, r=\frac{3}{7}$
  • B $a=2, r=\frac{3}{8}$
  • C $a=\frac{3}{2}, r=\frac{1}{2}$
  • D $a=3, r=\frac{1}{4}$
Solution:
2478 Upvotes Verified Answer
The correct answer is: $a=3, r=\frac{1}{4}$
Since, sum $=4$ and second term $=\frac{3}{4}$ $\Rightarrow \frac{a}{1-r}=4$, and $a r=\frac{3}{4}$ $\Rightarrow \frac{a}{1-\frac{3}{4 a}}=4$ $\Rightarrow(a-1)(a-3)=0$ $\Rightarrow a=1$ or $a=3$

$\begin{array}{l}

\Rightarrow \frac{a}{1-\frac{3}{4 a}}=4 \\

\Rightarrow(a-1)(a-3)=0 \\

\Rightarrow a=1 \text { or } a=3

\end{array}$

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