Question

Friedzz...
Please give me the correct answer
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

It is given that Two AP's have the same common difference.

⇒ Let the Same common difference of two AP's is d.

⇒ Let the first term of the first AP be 'a'.

⇒ Let the first term of the second AP be 'A'.

(i)

Now,

We know that nth term of an AP a(n) = a + (n - 1) * d.

Given that Difference between their 100th terms is 100.

⇒ a₁₀₀ - A₁₀₀ = 100

⇒ a + (100 - 1) * d - [A + (100 - 1) * d] = 100

⇒ a + 100d - d - [A + 100d + d] = 100

⇒ a  +100d - d - A - 100d + d = 100

⇒ a - A = 100    ------ (1)

(ii)

Difference between their 1000th terms:

⇒ a₁₀₀₀ - A₁₀₀₀:

⇒ a + (1000-1) * d - [A + (1000-1) * d]

⇒ a + 999d - [A + 999d]

⇒ a + 999d - A - 999d

⇒ a - A {From (1)}

⇒ 100.

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

Hope this helps!