Question

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

Answer 1

Let for the 1^st AP, the first term = a and common difference = d

T₁₀₀ = a + 99d

And for the 2^nd AP, the first term = a and common difference = d

T₁₀₀ = a + 99d

According to the condition

T₁₀₀ - T₁₀₀ = 100

a + 99d - (a + 99d) = 100

a - a = 100 

Let T₁₀₀₀ - T₁₀₀₀ = x

a + 999d - (a + 999d) = x

a - a = x

x = 100

The difference between the 1000^th terms is 100.