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

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Filo · Accepted Answer

Given that their 100th term's difference is 100Let the first no. of first series be a1​ and second series be a2​.then, a100​(1)−a100​(2)=100 --- 1)For 1st series ---- a100​=a1​+99d    2nd series ---- a100​=a2​+99dPut these values in (1)then, a1​+99d−(a2​+99d)=100a1​+99d−a2​−99d=100therefore, a1​−a2​=100 ---2)Then, the difference between their 1000th terms isfor 1st series --- a1000​=a1​+999dfor 2nd series --- a1000​=a2​+999dtheir 100th terms difference isa1000​(1)−a1000​(2)a1​+999d−(a2​+999d)a1​+999d−a2​−999dTherefore, we get the value a1​−a2​from (2), a1​−a2​=100Therefore, the difference between their 1000th terms is 100.

Question Text	Two APs have the same common difference. The difference between their $10 0^{t h}$ terms is $100$ , what is the difference between their $100 0^{t h}$ terms.
Answer Type	Text solution:1
Upvotes	150

Two APs have the same common difference. The difference between their $10 0^{t h}$ terms is $100$ , what is the difference between their $100 0^{t h}$ terms.

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