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)
G Gautam harsolia

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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