Question

Two arithmetic progression have the same common difference. The difference between their 100th terms is 100, What is the difference between their 1000th terms?

Answer 1

Here, we are given two A.P sequences which have the same common difference. Let us take the first term of one A.P. as a and of other A.P. as a’

Also, it is given that the difference between their 100^th terms is 100.

We need to find the difference between their 100^th terms

So, let us first find the 100^th terms for both of them.

Now, as we know,

So, for 100^th term of first A.P. (n = 100),

Now, for 100^th term of second A.P. (n = 100),

Now, we are given,

On substituting the values, we get,

Now, we need the difference between the 1000^th terms of both the A.P.s

So, for 1000^th term of first A.P. (n = 1000),

Now, for 1000^th term of second A.P. (n = 1000),

So,

Therefore, the difference between the 1000^th terms of both the arithmetic progressions will be.