# Two APs have the same common difference.the difference between their 100th terms is 100,what is the difference between their 1000th th term?

1
by rajnani
2 min
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2015-05-06T21:19:43+05:30
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
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