Question

Two AP’s have the same common difference. The difference between their 100^th terms 100, what is the difference between their 1000^th terms.

Options

• 200

• 150

• 100

• 55

Answer 1

100

Explanation:-

Let first term of first AP = a

Let first term of 2nd AP = a′

It is given that their common difference is same.

Let their common difference be d.

It is given that difference between their 100^th terms is 100. Using formula a_n = a + (n - 1) d, to find n^th term of arithmetic progression, we can say that

a + (100 - 1)d - (a′ + (100 - 1)d

= a + 99d - a′ - 99d = 100

⇒ a - a′ = 100     ....(1)

We want to find difference between their 1000^th terms which means we want to calculate:

a + (1000 - 1)d - (a′ + (1000 - 1)d

= a + 999d - a′ - 999d = a - a′

Putting equation (1) in the above equation we get,

a + (1000 - 1)d - (a′ + (1000 - 1)d)

= a + 999d - a′ - 999d

= a - a′ =100

Therefore, difference between their 1000^th terms would be equal to 100.