Question

Hey Friendz..

Two APs have the same common differnce . The difference between their 100th term is 100, what is the difference between their 1000th terms??

Answer 1

For ap1
=>100th term is
a+ 99d

=> For AP2
100th terms is
A+ 99D
here d=D

Difference = a +99d -A -99D
= a-A

Thus difference between their 1000th term will also be a-A as it is a constant.
The difference between any two corresponding terms of these two Ap's will be a-A

Answer 2

Let the first term of the first AP be a1.

Let the first term of the second AP be a2.

We know that nth term of an AP = a + (n - 1) * d

Given that Difference between their 100th term is 100.

= > (a1 + 99d) - (a2 + 99d) = 100

= > a1 - a2 = 100

----------------------------------------------------------------------------------------------------------------

Now,

Difference between their 1000th term:

= > (a1 + 999d) - (a2 + 999d)

= > a1 - a2

= > 100.

Hope this helps!