Question

If in a progression $a_1,a_2,a_3,...$ etc. $(a_r=a_{r+1})$ bears a constant ratio with $a_r.a_{r+1},$ then the terms of the progression are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. none of these.

Answer 1

Answer: (C)

Since $\frac{a_r-a_{r+1}}{a_r.a_{r+1}}$ constant for all $r$
$\Rightarrow \frac{1}{a_{r+1}}-\frac{1}{a_r}=$ constant for all $r$
$\Rightarrow a_1,a_2,a_3,.....$ are in $H.P$.