WBJEE · Maths · Sequences and Series
Five numbers are in HP. The middle term is 1 and the ratio of the second and the fourth terms is 2: 1 . Then, the sum of the first three terms is
- A \(\frac{11}{2}\)
- B 5
- C 2
- D \(\frac{14}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{11}{2}\)
Step-by-step Solution
Detailed explanation
Let \(a-2 d, a-d, a, a+d, a+2 d\) are in \(A P\). then \(\frac{1}{a-2 d} \cdot \frac{1}{a-d} \cdot \frac{1}{a} \cdot \frac{1}{a+d} \cdot \frac{1}{a+2 d}\) are in \(\mathrm{HP}\). Given, middle term \(=1\) \(\Rightarrow \quad \frac{1}{a}=1 \Rightarrow a=1\) and…
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