Two arithmetic sequences have the same common difference. The difference between their 100th terms is 100. What is the difference between their 1000th terms?
+128473 If they have the same common difference and the difference of their 100th terms is 100, then the first term difference is also 100
So.......the difference between their 1000th terms will also be = 100
To see this, let the first term of one series = n and the first term of the second series = n + 100
The difference of the series after ANY term =
(n + 100) + d ( n -1) = n + 100 + nd - d (1)
n + d ( n -1) = n + nd - d (2)
Subtract (2) from (1)
100 = the difference
