Class 10 Maths Arithmetic Progressions questions with solutions

Q 1 :

Ananya saves Rs. 24 during the first month Rs. 30 in the second month and Rs. 36 in the third month. She continues to save in this manner.

On the basis of above information answer the following questions.

Q. Whether the monthly savings of Ananya form an AP or not ? If yes then write the first term and common difference.

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(6)

Savings of Ananya are Rs. 24, Rs. 30, Rs. 36, ...

Since it is uniformly increasing by Rs. 6, therefore it forms an AP.

Here, a = 24, d = 30 – 24 = 6

Q 2 :

Ananya saves Rs. 24 during the first month Rs. 30 in the second month and Rs. 36 in the third month. She continues to save in this manner.

On the basis of above information answer the following questions.

Q. What is the amount that she will save in 15th month?

0%

(108)

$a_{15} = a + 14 d = 24 + 14 \times 6 = 24 + 84 = Rs. 108$

Q 3 :

Ananya saves Rs. 24 during the first month Rs. 30 in the second month and Rs. 36 in the third month. She continues to save in this manner.

On the basis of above information answer the following questions.

Q. In which month, will she save Rs. 66?

0%

(8)

$a_{n} = 66 \Rightarrow a + (n - 1) d = 66$

$\Rightarrow 24 + (n - 1) 6 = 66 \Rightarrow n - 1 = \frac{42}{6} = 7 \Rightarrow n = 8$

Q 4 :

Ananya saves Rs. 24 during the first month Rs. 30 in the second month and Rs. 36 in the third month. She continues to save in this manner.

On the basis of above information answer the following questions.

Q. What is the common difference of an AP whose nth term is 8 – 5n?

0%

(-5)

$a_{n} = 8 - 5 n$

$a_{1} = 8 - 5 = 3$

$a_{2} = 8 - 10 = - 2 \Rightarrow d = a_{2} - a_{1} = - 2 - 3 = - 5$

Q 5 :

A school has decided to plant some endangered trees on 51st World Environment Day in the nearest park. They have decided to plant those trees in few concentric circular rows such that each succeeding row has 20 more trees than the previous one. The first circular row has 50 trees.

Based on the above given information, answer the question :

Q. How many trees will be planted in the 10th row ?

0%

(230)

Here $a$ = 50 and $d$ = 20

Number of trees planted in 10th row = $a_{10}$ = 50 + 9 × 20 = 230

Q 6 :

A school has decided to plant some endangered trees on 51st World Environment Day in the nearest park. They have decided to plant those trees in few concentric circular rows such that each succeeding row has 20 more trees than the previous one. The first circular row has 50 trees.

Based on the above given information, answer the questions :

Q. How many more trees will be planted in the 8th row than in the 5th row ?

0%

(60)

Here $a = 50$ and $d = 20$

$a_{8} - a_{5} = 3 \times 20 = 60$

Q 7 :

A school has decided to plant some endangered trees on 51st World Environment Day in the nearest park. They have decided to plant those trees in few concentric circular rows such that each succeeding row has 20 more trees than the previous one. The first circular row has 50 trees.

Based on the above given information, answer the question :

Q. If 3200 trees are to be planted in the park, then how many rows are required ?

0%

(16)

Here $a = 50$ and $d = 20$

Let $S_{n} = 3200$

$\Rightarrow S_{n} = \frac{n}{2} [2 a + (n - 1) d] = 3200$

$\Rightarrow S_{n} = \frac{n}{2} [2 \times 50 + (n - 1) \times 20] = 3200$

$\Rightarrow n^{2} + 4 n - 320 = 0$

$\Rightarrow (n + 20) (n - 16) = 0$

Since, $n \neq - 20$

$∴$ $n = 16$

Hence, required number of rows are 16

Q 8 :

A school has decided to plant some endangered trees on 51st World Environment Day in the nearest park. They have decided to plant those trees in few concentric circular rows such that each succeeding row has 20 more trees than the previous one. The first circular row has 50 trees.

Based on the above given information, answer the question :

Q. If 3200 trees are to be planted in the park, then how many trees are still left to be planted after the 11th row ?

0%

(1550)

Required number of trees = $S_{n} - S_{11}$

$= 3200 - \frac{11}{2} [2 \times 50 + 10 \times 20] = 3200 - 1650 = 1550$

Hence, number of trees left are 1550

Q 9 :

In Mathematics, relations can be expressed in various ways. Matchstick patterns are an example of linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures.

Based on the above information, answer the following questions:

(i) Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP.

$a_{n} = 2 (n + 1)$
$a_{n} = 1 (n + 2)$
$a_{n} = 1 (2 + 2)$
$a_{n} = 3 (n + 2)$

1

2

3

4

(1)

The AP formed by the number of triangles in each figure is: 4, 6, 8, …

Here, a=4,??d=6-4=8-6=2

$The n^{t h} term of an AP is a_{n} = a + (n - 1) d \Rightarrow a_{n} = 4 + (n - 1) \times 2 = 4 + 2 n - 2 = 2 n + 2 = 2 (n + 1) S o, a_{n} = 2 (n + 1)$

Q 10 :

In Mathematics, relations can be expressed in various ways. Matchstick patterns are an example of linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures.

Based on the above information, answer the following questions:

(ii) Which figure has 61 matchsticks?

8th figure
7th figure
5th figure
4th figure

1

2

3

4

(1)

The AP formed by the number of matchsticks in the figure is:
12, 19, 26, …

Here, $a = 12, d = 19 - 12 = 26 - 19 = 7$

Let the nth figure have 61 matchsticks. Then:

$a_{n} = 61 12 + (n - 1) 7 = 61 (n - 1) 7 = 49 \Rightarrow n - 1 = 7 \Rightarrow n = 8$

The 8th figure has 61 matchsticks.

Topic Question Set

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Q 2 :

Ananya saves Rs. 24 during the first month Rs. 30 in the second month and Rs. 36 in the third month. She continues to save in this manner.

On the basis of above information answer the following questions.

Q. What is the amount that she will save in 15th month?

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Q 3 :

Ananya saves Rs. 24 during the first month Rs. 30 in the second month and Rs. 36 in the third month. She continues to save in this manner.

On the basis of above information answer the following questions.

Q. In which month, will she save Rs. 66?

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Q 4 :

Ananya saves Rs. 24 during the first month Rs. 30 in the second month and Rs. 36 in the third month. She continues to save in this manner.

On the basis of above information answer the following questions.

Q. What is the common difference of an AP whose nth term is 8 – 5n?

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