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

**Solution:**

The formula for n^{th} term of an AP is a_{n} = a + (n - 1) d

Here, a_{n} is the n^{th} term, a is the first term, d is the common difference and n is the number of terms.

For first A.P., a_{100} = a_{1} + (100 - 1) d

= a_{1} + 99d

a_{1000} = a_{1} + (1000 - 1)d

a_{1000} = a_{1} + 999d

For second A.P.,

b_{1000} = b_{1} + (100 - 1)d

= b_{1} + 99d

b_{1000} = b_{1} + (1000 - 1)d

= b_{1} + 999d

Given that, difference between 100^{th} term of these A.P.s = 100

Thus, we have

(a_{1} + 99d ) - (b_{1} + 99d ) = 100

a_{1} - b_{1} = 100 ...(1)

Difference between 1000th terms of these A.P.s

(a_{1} + 999d ) - (b_{1} + 999d ) = a_{1} - b_{1} ...(2)

From equation (1) & Equation (2),

This difference, a_{1} - b_{1} = 100

Hence, the difference between the 1000^{th} terms of these A.P. will be 100.

Answer: The difference between the 1000^{th} terms of these APs will be 100.

**Video Solution:**

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

### NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 12 - Chapter 5 Exercise 5.2 Question 12:

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

The difference between the 1000th terms of the given APs is 100 if the difference between their 100th terms is 100