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in Arithmetic Progression by (65.5k points)
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Two AP have the same common difference. The difference between their 100th terms is 100. what is the difference between their 1 000th terms?

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Having common difference ‘d’, the AP 

1st set a, a+d, a+2d 

2nd set b, b + d, b + 2d 

100th term of 1st set – 100th term of 2nd set = 100 

∴ a + 99d – (b + 99d) = 100 

a + 99d – b – 99d = 100 a – b= 100 

Similarly. 

1000th term of 1st set = 1 + 999d 

1000 th term of 2nd set = b + 999d 

Their difference 

= a + 999d – (b + 999d) 

= a + 999d – b – 999d 

= a – b.

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