Question

Find the common difference of the Arithmetic progression (A. P.)
1/a,3-a/3a

Answer 1

we know , common difference of an arithmetic progression is difference of two successive terms.

for example, if $a_0,a_1,a_2,....a_n$ are in arithmetic progression

then, common difference = $a_1-a_0=a_2-a_1=a_n-a_{n-1}$

here two successive terms of an arithmetic progression are ; 1/a , (3 - a)/3a

so, common difference = (3 - a)/3a - 1/a

= (3 - a - 3)/3a = -a/3a = -1/3

hence, common difference is -1/3

Answer 2

Given: Arithmetic progression = 1/a, 3-a/3a

To find:  common difference=?

Solution:

• As we know that  common difference is difference of two successive terms in an Arithmetic progression,

         eg. if a is first term and b is the second term so the common difference will be (b-a)

• So we have the two successive terms of an AP

                 1/a, 3-a/3a

• So the common difference of these terms are:

                 = 3-a/3a - 1/a

                 = 3-a/3a - 3/3a

                 = 3-a-3/3a

                 = -a/3a

                 = -1/3

Answer:

            So, the common difference obtained is -1/3