Question

Two $A{P}^{\prime }s$ have the same common difference. The difference between their ${100}^{th}$ terms is $100$. Find the difference between their ${1000}^{th}$ terms.

Answer 1

$1st$ AP

$a=a_{1}d=d{T}_{1}100=a_1+99d$

$2nd$ AP

$a=a_{2}d=d{T}_{2}100=a_2+99d$

$T_{1}100-T_{2}100=a_1-a_2=100T_{1}1000=a_1+999d{T}_{2}1000=a_2+999d{T}_{1}1000-T_{2}1000=a_1-a_2=100$