The common difference of A.P. $\frac{1}{3q} ,\frac{1-6q}{3q} ,\frac{1-12q}{3q} ,......$is:
$( A)\ q$
$( B)\ -q$
$( C)\ -2$
$( D)\ 2$

Given: An A.P. $\frac{1}{3q} ,\frac{1-6q}{3q} ,\frac{1-12q}{3q} ,......$

To do: To find the comman difference of the given A.P.

Solution: Given A.P. is,
$\frac{1}{3q} ,\frac{1-6q}{3q} ,\frac{1-12q}{3q} ,......$

As known, Comman difference$=$difference of two consecutive terms

$=\frac{1-6q}{3q} -\frac{1}{3q}$

$=\frac{1-6q-1}{3q}\\=\frac{-6q}{3q}$

$=-2$

$\therefore$ Option $( C)$ is correct.

 

Updated on: 10-Oct-2022

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