Question

Given A.P is $\frac{1}{3q},\frac{1-6q}{3q},\frac{1-12q}{3q}$. Find the common difference

• A. $1$
• B. $-1$
• C. $2$
• D. $-2$

Answer 1

Answer: (D)

$-2$

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

Then, $\frac{1}{3q},\frac{1}{3q}-\frac{6q}{3q},\frac{1}{3q}-\frac{12q}{3q}$ will also be in AP.

Which results in,

$\frac{1}{3q},\frac{1}{3q}-2,\frac{1}{3q}-4$

It can be seen clearly that the series is decreasing by the quantity (2)

Hence, the common difference is $-2$