Question

Two AP have the same common difference.The difference between their 100th term is 100.What is the difference between their 100th term?​

Answer 1

Given that 2 ap's have same common difference

given that their 100th terms difference is 100

let the first no. of first series be a1 and second series be a2

then, a(1)100 - a(2)100=100 ---- 1

for 1st series ---- a100=a1+99d

    2nd series ---- a100 = a2+99d

keep these values in (1)

then, 

a1+99d - (a2+99d) = 100

a1+99d-a2-99d=100

therefore, a1-a2 =100 ------------------------------------------- 2

then the difference between their 1000th terms is

for 1st series --- a1000 = a1+999d

for 2nd series --- a1000 = a2+999d

their 100th terms difference is

a(1)1000-a(2)1000

a1+999d-(a2+999d)

a1+999d-a2-999d

therefore we get the value a1-a2

from (2) a1-a2 = 100

therefore the difference between their 1000th terms is 100