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Two APs have the same common difference. The difference betwee

Question

Two APs have the same common difference. The difference between their $100^{t h}$ terms is 100, what is the difference between their $1000^{t h}$ terms?

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Henry Discussed

Two APs have the same common difference. The difference between their

100^{t h}

terms is 100, what is the difference between their

1000^{t h}

terms?

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Solution:

S_{1} : a_{1}, a_{2} \dots .. d

S_{2} : b_{1}, b_{2} \dots .. l

a_{100} - b_{100} = 100

a_{100} = a + (100 - 1) d

= a + 99 d

b_{100} = b + (100 - 1) l

= b + 99 l

a_{100} - b_{100} = 100

a - b = 100

a_{1000} - b_{1000}

a + 999 d - b - 999 l

a - b

=100

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Question Text	Two APs have the same common difference. The difference between their $100^{t h}$ terms is 100, what is the difference between their $1000^{t h}$ terms?
Answer Type	Text solution:1
Upvotes	150