Question

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

Answer 1

Answer:

100

Step-by-step explanation:

Answer 2

Answer:

100

Step-by-step explanation:

Let a₁ and a₂ be the first terms and d be the common difference.

tₙ = a + (n-1)d

For the first series.

tₐ = t₁₀₀= a₁ + 99d

For the 2nd series.

tₓ = t₁₀₀= a₂ + 99d

Given difference between 100th terms of two series is 100.

a₂ + 99d - (a₁ + 99d) = 100

=> a₂ - a₁ = 100.  =====================> Equation 1

Now for the first series, 1000th term is.

tₐ = t₁₀₀₀= a₁ + 999d

For the 2nd series,1000th term is

tₓ = t₁₀₀₀= a₂ + 999d

Difference = a₂ + 999d - (a₁ + 999d)

                  = a₂ - a₁  (∵ as per equation 1, a₂ - a₁  = 100)

                  = 100.