ML Aggarwal Arithmetic and Geometric Progression Exe-9.1 Class 10 ICSE Maths Solutions

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
Publications Avichal Publishig Company (APC)
Subject Maths
Class 10th
Chapter-9 Arithmetic and Geometric Progression(AP GP)
Writer ML Aggarwal
Book Name Understanding
Topics Solution of Exe-9.1 Questions
Edition 2022-2023

 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, \\ \frac { 5 }{ 2 } , 3, \\ \frac { 7 }{ 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 : –

Return to :- ML Aggarwal Solutions for ICSE Class-10

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