Read and download free pdf of CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set A. Download printable Mathematics Class 10 Worksheets in pdf format, CBSE Class 10 Mathematics Chapter 5 Arithmetic Progression Worksheet has been prepared as per the latest syllabus and exam pattern issued by CBSE, NCERT and KVS. Also download free pdf Mathematics Class 10 Assignments and practice them daily to get better marks in tests and exams for Class 10. Free chapter wise worksheets with answers have been designed by Class 10 teachers as per latest examination pattern

## Chapter 5 Arithmetic Progression Mathematics Worksheet for Class 10

Class 10 Mathematics students should refer to the following printable worksheet in Pdf in Class 10. This test paper with questions and solutions for Class 10 Mathematics will be very useful for tests and exams and help you to score better marks

### Class 10 Mathematics Chapter 5 Arithmetic Progression Worksheet Pdf

**Multiple Choice Questions **

**Question. The sum of first five terms of the AP: 3, 7, 11, 15, ... is:**

(a) 44

(b) 55

(c) 22

(d) 11

**Answer : B**

**Question. If the first term of an AP is 1 and the common difference is 2, then the sum of first 26 terms is**

(a) 484

(b) 576

(c) 676

(d) 625

**Answer : C**

**Question. If the sum to n terms of an AP is 3n2 + 4n, then the common difference of the AP is**

(a) 7

(b) 5

(c) 8

(d) 6

**Answer : D**

**Question. If a, b, c are in AP then ab + bc =**

(a) b

(b) b2

(c) 2b2

(d) 1/b

**Answer : C**

**Question. The sum of all natural numbers which are less than 100 and divisible by 6 is**

(a) 412

(b) 510

(c) 672

(d) 816

**Answer : D**

### Assertion-Reason Type Questions

**In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct ****choice as:**

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation ofassertion (A).

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

**Question. Assertion (A): Sum of the first 10 terms of the arithmetic progression –0.5, –1.0, –1.5,... is 27.5.
Reason (R): Sum of first n terms of an AP is given as S _{n} = n/2 [2a + (n – 1)d] where a = first term, d = common difference.**

**Answer : A**

**Question. Assertion (A): The sum of the first n terms of an AP is given by S _{n} = 3n^{2} – 4n. Then its nth term, a_{n} = 6n – 7.**

**Reason (R): nth term of an AP, whose sum of n terms is Sn, is given by a**

_{n}= S_{n}– S_{n–1}.**Answer : A**

**Question. Assertion (A): Sum of first hundred even natural numbers divisible by 5 is 500.
Reason (R): Sum of the first n terms of an AP is given by S _{n }= n/2 [a + l] where l = last term.**

**Answer : D**

### Case Study Based Questions

**I.** Pollution—A Major Problem: One of the major serious problems that the world is facing today is the environmental

pollution. Common types of pollution include light, noise, water and air pollution.

In a school, students thoughts of planting trees in and around the school to reduce noise pollution and air pollution.

**Condition I:** It was decided that the number of trees that each section of each class will plant be the same as the class in

which they are studying, e.g. a section of class I will plant 1 tree a section of class II will plant 2 trees and so on a section

of class XII will plant 12 trees.

**Condition II:** It was decided that the number of trees that each section of each class will plant be the double of the class

in which they are studying, e.g. a section of class I will plant 2 trees, a section of class II will plant 4 trees and so on a

section of class XII will plant 24 trees.

**Refer to Condition I**

**Question. The AP formed by sequence i.e. number of plants by students is**

(a) 0, 1, 2, 3, ..., 12

(b) 1, 2, 3, 4, ..., 12

(c) 0, 1, 2, 3, ..., 15

(d) 1, 2, 3, 4, ..., 15

**Answer : B**

**Question. If there are two sections of each class, how many trees will be planted by the students?**

(a) 126

(b) 152

(c) 156

(d) 184

**Answer : C**

**Question. If there are three sections of each class, how many trees will be planted by the students?**

(a) 234

(b) 260

(c) 310

(d) 326

**Answer : A**

**Refer to Condition II**

**Question. If there are two sections of each class, how many trees will be planted by the students?**

(a) 422

(b) 312

(c) 360

(d) 540

**Answer : B**

**Question. If there are three sections of each class, how many trees will be planted by the students?**

(a) 468

(b) 590

(c) 710

(d) 620

**Answer : A**

**II.** Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of ₹ 1,18,000 by paying every month starting with the first instalment of ₹ 1000. If he increases the instalment by ₹ 100 every month, answer the following:

**Question. The amount paid by him in 30th installment is**

(a) ₹ 3900

(b) ₹ 3500

(c) ₹ 3700

(d) ₹ 3600

**Answer : A**

**Question. The total amount paid by him upto 30 installments is**

(a) ₹ 37000

(b) ₹ 73500

(c) ₹ 75300

(d) ₹ 75000

**Answer : B**

**Question. What amount does he still have to pay after 30th installment?**

(a) ₹ 45500

(b) ₹ 49000

(c) ₹ 44500

(d) ₹ 54000

**Answer : C**

**Question. If total installments are 40, then amount paid in the last installment is**

(a) ₹ 4900

(b) ₹ 3900

(c) ₹ 5900

(d) ₹ 9400

**Answer : A**

**Question. The ratio of the 1st installment to the last installment is**

(a) 1 : 49

(b) 10 : 49

(c) 10 : 39

(d) 39 : 10

**Answer : B**

**ARITHMETIC PROGRESSIONS**

**Q.- Determine the general term of an A.P. whose 7**

^{th}term is –1 and 16th term 17.**Sol.**Let a be the first term and d be the common difference of the given A.P. Let the A.P. be a

_{1}, a

_{2}, a

_{3}, ....... an, .......

_{7}= – 1 and a

_{16}= 17

_{n}

**Q.- If five times the fifth term of an A.P. is equal to 8 times its eight term, show that its 13**

^{th}term is zero.**Sol**. Let a

_{1}, a

_{2}, a

_{3}, ..... , an, .... be the A.P. with its first term = a and common difference = d.

_{5}= 8a

_{8}

_{13}= 0

**Q.-**

**If m times mth term of an A.P. is equal to n times its nth term, show that the (m + n) term of the A.P. is zero.**

**Sol.**Let a be the first term and d be the common difference of the given A.P. Then, m times m

^{th}term = n times nth term

_{m}= na

_{n}

_{m+n}= 0

**Q.-**

**If the pth term of an A.P. is q and the qth term is p, prove that its nth term is (p + q – n).**

**Sol**Let a be the first term and d be the common difference of the given A.P. Then,

^{th}term = a + (n – 1) d

**SECTION A:**

_{n}=2n

^{2}forms an A.P.

^{th}term of an A.P is 5 – 2n.

^{2}+ 5n, then find its n

^{th}term.

^{2}+ bp, find its common difference.

^{th}term of the A.P. -2, -5, -8, …..

**SECTION B:**

^{th}term from the end of the A.P. 17, 14, 11, …. – 40.

^{th}term?

^{2}+ 3n. Find its 20

^{th}term.

**SECTION C:**

^{th}term is given by a

_{n}= 2 – 3n.

^{th}term of an A.P. is equal to n times its nth term, find its (m + n)

^{th}term.

^{th}and 10

^{th}terms of an A.P. are 13 and 25 respectively. Find the A.P.

^{th}term.

^{rd}term is four times its 12

^{th}term.

^{th}of an AP is equal to three times its third term. If 6th term is 22, find the AP.

^{th}term is 30.

^{th}term of an AP is 499 and 499

^{th}term is 9, find the term which is equal to zero.

**SECTION D:**

^{2}. If its p

^{th}term is –60, find the value of p. Also, find the 11

^{th}term of the AP.

^{st}term of an AP whose 11

^{th}term is 38 and 16

^{th}term is 73.

_{n}= 3 + 2n.

^{th},q

^{th}and r

^{th}terms of an AP are a , b and c respectively, then show that a(q – r) + b(r – p) + c(p – q) = 0.

**Please click on below link to download CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set A**

CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A |

CBSE Class 10 Maths Probabilty Worksheet |

## More Study Material

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