Question

Two APs have the same common difference is differences between their 100th term is 100 what is the difference between their 1000th term ?
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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

OR

let first term =a let first term =b
common difference=d common diff=d

a100= a+99d
b100= b+99d
a100-b100=a-b
a-b=100
a1000=a+999d
b1000=b+999d
a1000-b1000 =a-b
a-b=100
so the common difference is 100 answer



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