Question

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

Answer 1

Sol:
Let two A.P's have the first terms a , a' and common difference d.

Given that difference between their 100th term is 100.

then a + 99d - a' - 99d = 100

⇒ a - a' = 100.

Now difference between 1000 th term is

$\Rightarrow$ a + 999d - a' - 999d

$\Rightarrow$ = a - a'

$\Rightarrow$ = 100

∴ Difference between 1000 th term is 100.