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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Sequences and Series

BITSAT 2021 · Mathematics · Sequences and Series

Consider an infinite geometric series with first term a and common...

Consider an infinite geometric series with first term aa and common ratio rr. If its sum is 4 and the second term is 34\frac{3}{4}, then:

Options

  1. Aa=47,r=37a=\frac{4}{7}, r=\frac{3}{7}
  2. Ba=2,r=38a=2, r=\frac{3}{8}
  3. Ca=32,r=12a=\frac{3}{2}, r=\frac{1}{2}
  4. Da=3,r=14a=3, r=\frac{1}{4}

Correct answer

D. a=3,r=14a=3, r=\frac{1}{4}

Step-by-step solution

Since, sum =4=4 and second term =34⇒a1−r=4=\frac{3}{4}\Rightarrow \frac{a}{1-r}=4, and ar=34⇒a1−34a=4⇒(a−1)(a−3)=0⇒a=1a r=\frac{3}{4}\Rightarrow \frac{a}{1-\frac{3}{4 a}}=4\Rightarrow(a-1)(a-3)=0\Rightarrow a=1 or a=3a=3⇒a1−34a=4⇒(a−1)(a−3)=0⇒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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