Q : 12       Two APs have the same common difference. The difference between their   \small 100th terms is  \small 100, what is the difference between their \small 1000th terms?
 

Answers (1)

It is given that
Two APs have the same common difference and  difference between their   \small 100th terms is  \small 100
i.e.
a_{100}-a'_{100}= 100
Let common difference of both the AP's be d 
\Rightarrow a+99d-a'-99d=100
\Rightarrow a-a'=100 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - (i)
Now, difference between 1000th term is 
a_{1000}-a'_{1000}
\Rightarrow a+999d -a'-999d
\Rightarrow a-a'
\Rightarrow 100 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (using \ (i) )
Therefore, difference between 1000th term is 100

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