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in Arithmetic Progression by (56.3k points)

Two arithmetic progressions 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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Best answer

Let the two A.Ps be A.P1 and A.P2

For A.P1 the first term = a and the common difference = d

And for A.P2 the first term = b and the common difference = d

So, from the question we have

a100 – b100 = 100

(a + 99d) – (b + 99d) = 100

a – b = 100

Now, the difference between their 1000th terms is,

(a + 999d) – (b + 999d) = a – b = 100

Therefore, the difference between their 1000th terms is also 100.

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