# two AP have the same common difference.the difference between their 100th terms is 100, what is the difference between their 1000th term ?

Let the second AP be represented as TB = a2 + (n2-1)d.

Now , 100th term of TA is TA100 = a1 + 99d

Similarly, 100th term of TB is TB100 = a2+99d

TB100 – TA100 = (a2 – a1) = 100

Therefore,

TA1000 – TB1000 = (a2 + 999d) – (a1 + 999d)

The difference is (a2 – a1) = 100