First slide

Arithmetic progression

Question

If $a, \frac{1}{b}, c and \frac{1}{p}, q, \frac{1}{r}$ form two arithmetic progressions of the same common difference, then a, q, c are in A.P. if

Moderate

A

p, b, r are in A.P.
B

$\frac{1}{p}, \frac{1}{b}, \frac{1}{r} areinA . P .$
C

p, b, r are in G.P
D

none of these

Solution

Since a, q and c are in A.P., so
$\begin{array}{l} 2 q = a + c \\ \Rightarrow \frac{1}{p} + \frac{1}{r} = \frac{2}{b} \\ \Rightarrow \frac{1}{p}, \frac{1}{b}, \frac{1}{r} are in A.P. \end{array}$

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