# CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 8 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 3**:

Which term of the AP: … is ?

**Answer**:

First term , Common difference and

Using formula *d*, to find term of arithmetic progression,

,

It means term of the given AP is equal to .

**Question 4**:

Find the number of terms in each of the following APs:

(i)

(ii)

**Answer**:

(i)

First term , Common difference

And

Using formula , to find nth term of arithmetic progression,

Therefore, there are terms in the given arithmetic progression.

(ii)

First term , Common difference

And

Using formula , to find nth term of arithmetic progression,

Therefore, there are terms in the given arithmetic progression

**Question 5**:

Check whether is a term of the AP:

**Answer**:

Let is the n^{th} of AP which means that

Here, First term , Common difference

Using formula , to find term of arithmetic progression,

But, n cannot be in fraction.

Therefore, our supposition is wrong. cannot be term in AP.

**Question 6**:

An AP consists of terms of which term is and the last term is . Find the term.

**Answer**:

An AP consists of 50 terms and the term is equal to and

Using formula , to find term of arithmetic progression,

And

These are equations consisting of two variables.

Using equation , we get

Putting value of *a* in the equation ,

Putting value of *d* in the equation, ,

Therefore, First term and Common difference

To find term, we use formula

which is used to find n^{th} term of arithmetic progression,

Therefore, term of AP is equal to