Two arithmetic progressions have the same common difference. The diffe

1.	Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
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 1000^th terms is, (a + 999d) – (b + 999d) = a – b = 100 Therefore, the difference between their 1000^th terms is also 100.

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

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 1000^th terms is,

(a + 999d) – (b + 999d) = a – b = 100

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