Question

Two ap's have same common difference. The difference between their 100th term is 100 what is the difference between their 1000th term​

Answer 1

Since they have common differences their 1000th terms difference will be 1000 only

Answer 2

Let a and A be the first term of the two APs and d be their common difference. Then,

$\longrightarrow$$\sf\red{a100 - A100 = 100}$

$\longrightarrow$$\sf\red{(a+99d)-(A+99d=100}$

$\longrightarrow$$\sf\red{a-A=100}$

Now,

$\sf\green{a1000-A1000=(a+999d)-(A+999d)=a-A=100}$

Hence, the difference between the 1000th terms of the two APs is also 100.