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 by
an = 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.
Rate this question :