Question

Which of the following sequences are arithmetic progressions . For those which are arithmetic progressions, find out the common difference.

`1/2, 1/4, 1/6, 1/8 ......`

Answer 1

In the given problem, we are given various sequences.

We need to find out that the given sequences are an A.P or not and then find its common difference (d)

`1/2, 1/4, 1/6, 1/8 ......`

Here,

First term (a) = 1/2

`a_3 = 1/4`

`a_2= 1/6`

Now, for the given to sequence to be an A.P,

The common difference (d) = `a_1 - a = a_2 - a_1`

here

`a_1 - a =1/4 - 1/2`

`= (1 - 2)/4`

`= (-1)/4`

Also

`a_2 - a_1 = 1/6 - 1/4`

`= (2 - 3)/12`

`= (-1)/12`

Since  `a_1 - a = a_2 - a_1`

Hence, the given sequence is not an A.P