Question

two APs have the same common difference. the difference between their 100th terms is 100, what is the differnce their 1000th terms?

Answer 1

let the first term of first AP be a. let the first term of second AP be a'. 100th term of first AP= a+99d. 100th term of second AP = a'+99d. difference between their 100th terms is 100. (a'+99d)-(a+99d) = 100. a'-a=100. now difference between their 1000th term = (a'+999d)-(a+999d)=a'-a. But a'-a=100. therefore difference between their 1000th terms is 100