Question

2 APs have the same common difference the difference between the 100 term is 100 what is the difference between their 1000 term.

Answer 1

let the first terms of the two ap be a and a'
given that common difference is equal (=d)
diff. btw their 100th terms is..
(a'+99d)-(a+99d)

a' +99d -a-99d=100
a'-a=100
a'=100+a------(i)
..now we have tofind the diff between their 1000th terms..
ie. ..(a'+999d)-(a+999d)
=a'+999d-a-999d
=a'-a=100 ... from (i)
so..required answer=100

Answer 2

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