**CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.3 Question 3**

**3. In an AP**

**(i) **given , find n and .

**(ii) **given , find d and .

**(iii) **given , find a and .

**(iv) **given , , find d and .

**(v) **given , find a and .

**(vi) **given , find n and .

**(vii) **given , find n and d.

**(viii) **given , find n and a.

**(ix) **given , find d.

**(x) **given , and there are total of 9 terms. Find a.

**Solution (i)**

Given , find n and .

Using formula , to find nth term of arithmetic progression, we can say that

**Applying formula**, to find sum of n terms of AP, **we get**

Therefore, and

**Solution (ii)**

Given , find d and .

**Using formula** , to find nth term of arithmetic progression, **we can say that**

**Applying formula**, to find sum of n terms of AP, **we get**

Therefore, and

**Solution (iii)**

Given , find a and .

**Using formula** , to find nth term of arithmetic progression, **we can say that**

Applying formula, to find sum of n terms of AP, we get

Therefore, and

**Solution (iv)**

Given , , find d and .

**Using formula** , to find nth term of arithmetic progression, **we can say that**

**(1)**

**Applying formula, ** to find sum of n terms of AP, **we get**

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

**Using formula** , to find nth term of arithmetic progression, **we can say that**

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

Therefore, and

**Solution (v)**

Given , find a and .

**Applying formula**, to find sum of n terms of AP, **we get**

**Using formula** , to find nth term of arithmetic progression, **we can say that**

Therefore, and

** **

**Solution (vi)**

Given , find n and .

**Applying formula**, to find sum of n terms of AP, **we get**

We discard negative value of n because here n cannot be in negative or fraction. The value of n must be a positive integer.

Therefore,

Using formula , to find nth term of arithmetic progression, we can say that

Therefore, and

** Solution (vii)**

Given , find n and d.

**Using formula** , to find nth term of arithmetic progression, **we can say that**

**(1)**

**Applying formula**, to find sum of n terms of AP, **we get**

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

Putting value of in equation **(1), **we get

Therefore, and

** **

**Solution (viii)**

Given , find n and a.

**Using formula** , to find nth term of arithmetic progression, **we can say that**

**(1)**

**Applying formula**, to find sum of n terms of AP, **we get**

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

Here, we cannot have negative value of . Therefore, we discard negative value of which means .

Putting value of in equation number **(1)**, we get

Therefore, and

**Solution (ix)**

Given , find d.

**Applying formula**, to find sum of n terms of AP, **we get**

**Solution (x)**

Given , and there are total of 9 terms. Find a.

**Applying formula**, ,** to find sum of n terms, we get**