JEE Mains · Maths · STD 11 - 8. sequence and series
If \(b\) is the first term of an infinite \(G.P\) whose sum is five, then \(b\) lies in the interval
- A \(\left( { - \infty ,-10} \right)\)
- B \(\left( {10,\infty } \right)\)
- C \(\left( {0,10} \right)\)
- D \(\left( { - 10,0} \right)\)
Answer & Solution
Correct Answer
(C) \(\left( {0,10} \right)\)
Step-by-step Solution
Detailed explanation
First term \(=b\) and commom ration \(=r\) For infinite series, Sum \( = \frac{b}{{1 - r}} = 5\) \( \Rightarrow b = 5\left( {1 - r} \right)\) So, interval of \(b = (0,10)\) as, \( - 1 < r < 1\) for infinite \(G.P.\)
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