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

$a_n=a+(n-1)d$

$a_{100}=a+(100-1)d$

$a_{100}=a+99d$

Similarly

$b_{100}=b+99d$

Given that,

$a_{100}-b_{100}=100$

$a+99d-b-99d=100$

$a-b=100$

Now we have to find

$a_{1000}-b1000$

$=a+999d-b-999d$

$=a-b$

$\therefore a_{1000}-b1000=a-b=100$

So, the difference between 1000th terms is 100