# CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 14 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 3**:

If the third and the ninth terms of an AP are and respectively, which term of this AP is zero?

**Answer**:

It is given that 3^{rd} and 9^{th} term of AP are 4 and respectively.

It means and

Using formula , to find term of arithmetic progression,

These are equations in two variables.

Using equation , we can say that

Putting value of *a* in other equation ,

Putting value of in equation ,

Therefore, first term and Common Difference

We want to know which term is equal to zero.

Using formula to find term of arithmetic progression,

Therefore, term is equal to .

**Question 4**:

Two AP՚s have the same common difference. The difference between their terms is , what is the difference between their terms.

**Answer**:

Let first term of 1^{st} AP

Let first term of 2^{nd}

It is given that their common difference is same.

Let their common difference be .

It is given that difference between their terms is .

Using formula , to find n^{th} term of arithmetic progression,

We want to find difference between their

1000^{th} terms which means we want to calculate:

Putting equation (1) in the above equation,

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

**Question 5**:

How many three-digit numbers are divisible by 7?

**Answer**:

We have AP starting from because it is the first three-digit number divisible by .

AP will end at because it is the last three-digit number divisible by .

Therefore, we have AP of the form

Let is the n^{th} term of AP.

We need to find n here.

First term , Common difference

Using formula , to find term of arithmetic progression,

It means is the term of AP.

Therefore, there are terms in AP.