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, , 3, ,……**

**(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 = 1^{2} = 1

Then, difference d = 3^{2} – 1^{2} = 9 – 1 = 8

5^{2} – 3^{2} = 25 – 9 = 16

7^{2} – 5^{2} = 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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