**CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.1 Question 4**

**4. Which of the following are APs? If they form an AP, find the common difference d and write three **

**more terms.**

(i)

(ii)

(iii) (iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

(xiii)

(xiv)

(xv)

**Solution (i)**

It is not an AP because difference between consecutive terms is not same.

**Example:**

**Solution (ii)**

It is an AP because difference between consecutive terms is same.

Common difference (d) =

Fifth term =

Sixth term =

Seventh term =

Therefore, next three terms are and

**Solution (iii)**

It is an AP because difference between consecutive terms is same.

Common difference (d) =

Fifth term =

Sixth term =

Seventh term =

Therefore, next three terms are and

**Solution (iv)**

It is an AP because difference between consecutive terms is constant.

Common difference (d) = 4

Fifth term = 2 + 4 = 6

Sixth term = 6 + 4 = 10

Seventh term = 10 + 4 = 14

Therefore, next three terms are and

**Solution (v)**

It is an AP because difference between consecutive terms is constant.

Common difference (d) =

Fifth term =

Sixth term =

Seventh term =

Therefore, next three terms are and

**Solution (vi)**

It is not an AP because difference between consecutive terms is not constant.

**Example:**

**Solution (vii)**

It is an AP because difference between consecutive terms is constant.

Common difference (d) =

Fifth term =

Sixth term =

Seventh term =

Therefore, next three terms are and

**Solution (viii)**

It is an AP because difference between consecutive terms is constant.

Common difference (d) = 0

Fifth term =

Sixth term =

Seventh term =

Therefore, next three terms are and

**Solution (ix) **

It is not an AP because difference between consecutive terms is not constant.

**Example:**

**Solution (x) **

It is an AP because difference between consecutive terms is constant.

Common difference (d) = a

Fifth term =

Sixth term =

Seventh term =

Therefore, next three terms are and

**Solution (xi)**

It is not an AP because difference between consecutive terms is not constant.

**Example:**

**Solution (xii)**

Therefore, sequence is like

It is an AP because difference between consecutive terms is constant.

Common difference (d) =

Fifth term =

Sixth term =

Seventh term =

Therefore, next three terms are and

**Solution (xiii)**

It is not an AP because difference between consecutive terms is not constant.

**Example:**

**Solution (xiv)**

It is not an AP because difference between consecutive terms is not constant.

**Example:**

**Solution (xv)**

Therefore, sequence is like

It is an AP because difference between consecutive terms is constant.

Common difference (d) =

Fifth term =

Sixth term =

Seventh term =

Therefore, next three terms are and