Question

Two aps have the same common difference the difference between the hundred term is 100 what is the difference

Answer 1

Let the common difference of two AP's be d, their first terms as a and a'

nth term of both the AP's will be given byan = a + (n - 1) d

a'n = a' + (n - 1) d

Now 100th term of 1st AP will be given by: a100 = a + (100 - 1) d = a + 99d

100th term of second AP will be given by: a'100 = a' + (100 - 1) d = a' + 99d

Given, a100 - a'100 = (a + 99 d) - (a' + 99 d)

⇒a100 - a'100 = (a - a')

So, difference does not depend on number of terms.Thus, a1000 - a'1000 = 100 = a100-a'100

So the difference between their 1000th terms is 100.

Hope it helps uh....❤