Consider an infinite geometric series with first term ' \( a \) ' and common ratio ' \( r \) '. If the sum…

Consider an infinite geometric series with first term ' \( a \) ' and common ratio ' \( r \) '. If the sum is \( 4 \) and
the second term is \( \frac{3}{4} \), then
  1. \( a=\frac{4}{7}, r=\frac{3}{7} \)
  2. \( a=3, r=\frac{1}{4} \)
  3. \( a=2, r=\frac{3}{8} \)
  4. \( a=\frac{3}{2}, r=\frac{1}{2} \)

Solution

Given that, first term is a and common ratio is \( r \).
and \( t_{2}=\frac{3}{4} \) \( \Rightarrow a r=\frac{3}{4} \rightarrow(1) \)
Now, \( 4=\frac{a}{1-r} \Rightarrow a=4-4 r \)
\( \Rightarrow 4 r=4-a \rightarrow(2) \)
From Eqs. (1) and (2), we get
\( a=3, r=\frac{1}{4} \)

Asked in: TEST SERIES MHT-CET Full Test 6

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