Question

find the common difference of an ap 1/a ,3-a/3a , 3-2a/3a

Answer 1

common difference = T1-T2

i.e 3-a/3a -1/a =

take lcm first

3-a-3/3a

-a/3a

= -1/3

Hopefully u get it

Answer 2

Answer:

$\textbf{The common difference of an A.P. , d = }\bf\frac{-1}{3}$

Step-by-step explanation:

Common difference is defined as a difference between any two consecutive terms of an A.P.

The terms of an A.P. are given to be :

$\frac{1}{a},\frac{3-a}{3a},\frac{3-2a}{3a}$

Common difference :

$d=a_2-a_1\\\\\implies d=\frac{3-a}{3a}-\frac{1}{a}\\\\\implies d =\frac{3-a-3}{3a}\\\\\implies d=\frac{-a}{3a}\\\\\implies d=\frac{-1}{3}$

$\text{Also, d = }a_3-a_2\\\\\implies d=\frac{3-2a}{3a}-\frac{3-a}{3a}\\\\\implies d=\frac{3-2a-3+a}{3a}\\\\\implies d=\frac{-a}{3a}\\\\\implies d=\frac{-1}{3}$

$\textbf{Hence, the common difference of an A.P. , d = }\bf\frac{-1}{3}$