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

Given that the 2 AP series has same common difference (d)

Let x, x+d, x+2d,…. X+(n-1)d &

y, y+d, y+2d,…..y+(n-1)d are the two A.P series

given that the difference between their 100th terms is 100

that is,

x+(100-1)d – (y+(100-1)d) = 100

x-y = 100

The difference between their 1000^th term is

= x+(1000-1)d –(y+(1000-1)d)

= x-y

We know that value from previous equation

= 100

∴ The difference between their 1000th terms is 100