WBJEE · Maths · Sequences and Series
If for the series \(a_1, a_2, a_3, \ldots\). etc, \(a_r-a_{r+1}\) bears a constant ratio with \(a_r a_{r+1} ;\) then \(a_1, a_2, a_3 \ldots\). are in
- A A.P.
- B G.P.
- C H.P.
- D Any other series
Answer & Solution
Correct Answer
(C) H.P.
Step-by-step Solution
Detailed explanation
Hint: \(\frac{a_{\mathrm{r}}-a_{r+1}}{a_{\mathrm{r}} a_{r+1}}=K(\) constant\() \Rightarrow \frac{1}{a_{\mathrm{r}+1}}-\frac{1}{a_{\mathrm{r}}}=K \quad \therefore \frac{1}{a_1}, \frac{1}{a_2}, \frac{1}{a_3}, \ldots \ldots\). is an A.P \(\Rightarrow a_1, a_2, a_3, \ldots\) is a H.P
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