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 with the Arithmetic Progression and we have to find the missing terms.
(i) 2, _, 26
We know that the nth term of an AP is given by, aₙ = a + (n - 1)d
Let the common difference be d
First term a = 2
Third term = a + (3 - 1)d = 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
The missing term in the box is 14.
ii) _, 13, _ , 3
aₙ = a + (n - 1)d
a₂ = 13, a₄ = 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 equations (1) and (2) to find a and d.
On subtracting equation (1) from equation (2), we get
a + 3d - (a + d) = 3 - 13
3d - d = 3 - 13
2d = - 10
d = - 5
Putting d = -5 in equation (1)
a + (- 5) = 13
a - 5 = 13
a = 18
Third term = a + (3 - 1)d = a + 2d
= 18 + 2(-5) = 8
The missing terms in the boxes are 18 and 8 respectively.
iii) 5, _ , _ , 9 ½
aₙ = a + (n - 1)d
First term a = 5
Fourth term, a₄ = 9 ½ = 19/2
Fourth term a₄ = a + (4 - 1) d
5 + 3d = 19/2
6d = 9
d = 3/2
Second term = a₂ = a + d
= 5 + 3/2
= 13/2
Third term, a₃ = a + 2d
= 5 + 2 × (3/2)
= 5 + 3
= 8
The missing terms in the boxes are 13/2 and 8 respectively.
iv) - 4, _ , _ , _ , _ , 6
aₙ = a + (n - 1)d
First term a = - 4
Sixth term a₆ = 6
a + (6 - 1)d = 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
The missing terms are - 2, 0, 2, 4.
v) _ , 38, _ , _ , _ , - 22
aₙ = a + (n - 1)d
Let the first term be = a
Common difference = d
Second term = 38 (Given)
a + (2 - 1)d = a + d = 38 ....(1)
Sixth term = - 22 (Given)
a + (6 - 1)d = a + 5d = - 22 ....(2)
On Subtracting equation (1) from equation (2) for a and d, we get
a + 5d - (a + d) = -2 2 - 38
4d = - 60
d = - 15
Put the value of d in equation (1)
a - 15 = 38
a = 53
Third term = a + (3 - 1)d = a + 2d
= 53 + 2(-15) = 23
Fourth term = a + 3d
= 53 + 3(-15) = 8
Fifth term = a + 4d
= 53 + 4(-15) = - 7
The missing terms are 53, 23, 8, - 7.
☛ Check: NCERT Solutions Class 10 Maths Chapter 5
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
Summary:
In the following AP, the missing terms in the boxes: i) 2, _, 26 ii) _, 13, _ , 3 iii) 5, _ , _ , 9 ½ iv) - 4, _ , _ , _ , _ , 6 v) _ , 38, _ , _ , _ , - 22 are i) 14 ii) 18 and 8 iii) 13/2 and 8 iv) -2, 0, 2 and 4 v) 53, 23, 8 and -7
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