Question

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

Answer 1

Yet $n^{th}$ term of list $A.P$ be $a_n$

Yet $n^{th}$ tern second $A.P$ be $b_n$

Yet common difference be $d$

$a_{100}-b_{100}=(a_1+aad)-(b_1+aaad)$

$a_1-b_1=100$

$a_{1000}-b_{1000}=(a_1+aaad)-(b_1+aaad)$

$=a_1-b_1$

$a_{1000}-b_{1000}=100$