**CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.2 Question 12**

**12. Two AP's have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms.**

**Solution:**

Let first term of first AP =

Let first term of 2nd AP =

It is given that their common difference is same. Let their common difference be .

It is given that difference between their 100th terms is 100. Using formula , to find nth term of arithmetic progression, we can say that

** (1)**

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

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

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