ML Aggarwal Arithmetic and Geometric Progression Exe-9.1 Class 10 ICSE Maths Solutions . We Provide Step by Step Answer of Exe-9.1 Questions for Arithmetic and Geometric Progression(AP GP) as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-10.
ML Aggarwal Arithmetic and Geometric Progression Exe-9.1 Class 10 ICSE Maths Solutions
| Board | ICSE |
| Subject | Maths |
| Class | 10th |
| Chapter-9 | Arithmetic and Geometric Progression |
| Writer / Book | Understanding |
| Topics | Solutions of Exe-9.1 |
| Academic Session | 2024-2025 |
Arithmetic and Geometric Progression Exe-9.1
(ML Aggarwal AP GP Class 10 ICSE Maths Solutions)
page-166
Question- 1. For the following A.P.s, write the first term a and the common difference d:
(i) 3, 1, – 1, – 3, …
(ii) 1/3, 5/3, 9/3, 13/3, ….
(iii) – 3.2, – 3, – 2.8, – 2.6, …
Answer:
(i) 3, 1, -1, -3, …
Here first term (a) = 3
and the common difference (d)
= 1 – 3 = -2,
– 1 – 1 = -2,…
= -2
(ii) 1/3, 5/3, 9/3, 13/3, ….
The first term a = 1/3
Then, difference d = 5/3 – 1/3 = (5 – 1)/3 = 4/3
9/3 – 5/3 = (9 – 5)/3 = 4/3
13/3 – 9/3 = (13 – 9)/3 = 4/3
(iii) – 3.2, – 3, – 2.8, – 2.6, …
The first term a = -3.2
Then, difference d = -3 – (-3.2) = -3 + 3.2 = 0.2
-2.8 – (-3) = -2.8 + 3 = 0.2
-2.6 – (-2.8) = -2.6 + 2.8 = 0.2
Question -2. Write first four terms of the A.P., when the first term a and the common difference d are given as follows :
(i) a = 10, d = 10
(ii) a = – 2, d = 0
(iii) a = 4, d = – 3
(iv) a = 1/2, d = – 1 /6
Answer:
(i) a = 10, d = 10
First term a = 10
Common difference d = 10
Then the first four terms are = 10 + 10 = 20
20 + 10 = 30
30 + 10 = 40
Hence, first four terms are 10, 20, 30 and 40
(ii) a = -2, d = 0
First term a = -2
Common difference d = 0
Then the first four terms are = -2 + 0 = -2
-2 + 0 = -2
-2 + 0 = -2
Hence, first four terms are -2, -2, -2 and -2.
(iii) a = 4, d = – 3
First term a = 4
Common difference d = -3
Then the first four terms are = 4 + (-3) = 4 – 3 = 1
1 + (-3) = 1 – 3 = – 2
-2 + (-3) = -2 – 3 = – 5
Hence, first four terms are 4, 1, -2 and -5.
(iv) a = 1/2, d = – 1 /6
First term a = ½
Common difference d = -1/6
Then the first four terms are = ½ + (-1/6) = ½ – 1/6 = (3 – 1)/6 = 2/6 = 1/3
1/3 + (-1/6) = 1/3 – 1/6 = (2 – 1)/6 = 1/6
1/6 + (-1/6) = 1/6 – 1/6 = 0
Hence, first four terms are ½, 1/3, 1/6 and 0.
Question -3. Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms :
(i) 4, 10, 16, 22,…
(ii) – 2, 2, – 2, 2,…..
(iii) 2, 4, 8, 16,….
(iv) 2, 
(v) – 10, – 6, – 2, 2,….
(vi) 1², 3², 5², 7²,….
Answer:
(i) 4, 10, 16, 22,…
Here a = 4, d = 10 – 4 = 6, 16 – 10 = 6, 22 – 16 = 6
∵ common difference is same
∵ It is in A.P
and next three terms are 28, 34, 40
(ii) – 2, 2, – 2, 2,…..
First term a = -2
Then, difference d = -2 – 2 = – 4
-2 – 2 = -4
2 – (-2) = 2 + 2 = 4
common difference d is not same in the given numbers.
Hence, It is not A.P.
(iii) 2, 4, 8, 16,….
First term a = 2
Then, difference d = 4 – 2 = 2
8 – 4 = 4
16 – 8 = 8
Therefore, common difference d is not same in the given numbers.
Hence, the numbers are not form A.P.
(iv) 2, 5/2, 3, 7/2, …
First term a = 2
Then, difference d = 5/2 – 2 = (5 – 4)/2 = ½
3 – 5/2 = (6 – 5)/2 = ½
7/2 – 3 = (7 – 6)/2 = ½
Therefore, common difference d = ½
Hence, the numbers are form A.P.
(v) – 10, – 6, – 2, 2,….
First term a = -10
Then, difference d = -6 – (- 10) = – 6 + 10 = 4
-2 – (-6) = – 2 + 6 = 4
2 – (-2) = 2 + 2 = 4
Therefore, common difference d = 4
Hence, the numbers are form A.P.
(vi) 1², 3², 5², 7²,….
First term a = 12 = 1
Then, difference d = 32 – 12 = 9 – 1 = 8
52 – 32 = 25 – 9 = 16
72 – 52 = 49 – 25 = 24
Therefore, common difference d is not same in the given numbers.
Hence, the numbers are not form A.P.
— : End of ML Aggarwal Arithmetic and Geometric Progression Exe-9.1 Class 10 ICSE Maths Solutions : –
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