Question

Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is

Options

• 11

• 3

• 8

• 5

Answer 1

Here, we are given two A.P.’s with same common difference. Let us take the common difference as d.

Given,

First term of first A.P. (a) = 8

First term of second A.P. (a_’) = 3

We need to find the difference between their 30^th terms.

So, let us first find the 30^th term of first A.P.

`a_30 =  a + ( 30 -1) d`

       = 8 + 29 d           ...........(1) 

Similarly, we find the 30^th term of second A.P.

`a'_(30) =  a '+ ( 30 -1) d`

         = 3 + 29 d            ...............(2)

Now, the difference between the 30^th terms is,

`a_30 - a'_(30) = (8 + 29d) - ( 3 + 29 d) `

                   = 8 + 29 d - 3 - 29 d

                   = 8 -3

                    = 5 

Therefore, `a_30 - a'_(30) = 5`