# In the following APs, find the missing terms in the boxes:

i) 2, _, 26

ii) _, 13, _ , 3

iii) 5, _ , _ , 9 ½

iv) - 4, _ , _ , _ , _ , 6

v) _ , 38, _ , _ , _ , - 22

**Solution:**

We are given Arithmetic Progression and we have to find the missing terms.

(i) a_{n} = a + (n - 1)d

Let common difference be d

First term a = 2

Third term = a + 2d = 2 + 2d

Third term = 26 (Given)

2 + 2d = 26

2d = 26 - 2

2d = 24

d = 12

Second term = a + d

= 2 + 12

= 14

Answer: The missing term in the box is 14.

ii) a_{n} = a + (n - 1)d

a_{2} = 13, a_{4} = 3

Second term = 13

a + (2 - 1) d = 13

a + d = 13 ....(1)

Fourth term = 3

a + (4 - 1) d = 3

a + 3d = 3 ....(2)

Solve (1) and (2) for a and d.

On subtracting Equation (2) from Equation (1), we get

3d - d = 3 - 13

2d = - 10

d = - 5

Putting d in equation (1)

a + (- 5) = 13

a - 5 = 13

a = 18

Third term = 18 - 10 = 8

Answer: The missing terms in the boxes are 18 and 8 respectively.

iii) First term a = 5

Fourth term, a_{4} = 9 ½ = 19 / 2

Fourth term a_{4} = a + (4 - 1) d

5 + 3d = 19 / 2

6d = 9

d = 3 / 2

Second term = a_{2} = a + d

= 5 + 3 / 2

= 13 / 2

Third term, a_{3} = a + 2d

= 5 + 2 × 3

= 5 + 3

= 8

Answer: The missing terms in the boxes are 13/2 and 8 respectively.

iv)

First term, a = - 4

Sixth term, a_{6} = 6

a + 5d = 6

- 4 + 5d = 6

5d = 10

d = 2

Second term a + d = - 4 + 2 = - 2

Third term a + 2d = - 4 + 4 = 0

Fourth term a + 3d = - 4 + 6 = 2

Fifth term a + 4d = - 4 + 8 = 4

Answer: The missing terms are - 2, 0, 2, 4.

v) Let the first term be = a

Common difference = d

Second term = 38 (Given)

a + d = 38 ....(1)

Sixth term = - 22 (Given)

a + 5d = - 22 ....(2)

On Subtracting (2) from (1) for a and d, we get

4d = - 60

d = - 15

Put the d value in equation (1)

a - 15 = 38

a = 53

Third term = a + 2d

= 53 - 30 = 23

Fourth term = a + 3d

= 53 - 45 = 8

Fifth term = a + 4d

= 53 - 60 = - 7

Answer: The missing terms are 53, 23, 8, - 7 respectively.

**Video Solution:**

## In the following AP, find the missing terms in the boxes: i) 2, _, 26 ii) _, 13, _ , 3 iii) 5, _ , _ , 9 ½ iv) - 4, _ , _ , _ , _ , 6 v) _ , 38, _ , _ , _ , - 22

### NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 3 - Chapter 5 Exercise 5.2 Question 3:

In the following AP, find the missing terms in the boxes: i) 2, _, 26 ii) _, 13, _ , 3 iii) 5, _ , _ , 9 ½ iv) - 4, _ , _ , _ , _ , 6 v) _ , 38, _ , _ , _ , - 22

The missing terms are i) 14 ii) 18 and 8 iii) 13/2 and 8 iv) -2, 0, 2, 4 v) 53, 23, 8 -7