Question

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

Answer 1

Let the first A.P be: 

a, a + d, a + 2d, …….. 

Second A.P be: 

b, b + d, b + 2d, b + 3d, ……… 

Also, general term, a_n = a + (n – 1)d 

Given that, a₁₀₀ – b₁₀₀ = 100 

⇒ a + 99d – (b + 99d) = 100 

⇒ a – b = 100 

Now the difference between their 1000^th terms,

∴ The difference between their 1000^th terms is (a – b) = 100. 

Note: If the common difference for any two A.Ps are equal then difference between n^th terms of two A.Ps is same for all natural values of n.