# CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set D

Read and download free pdf of CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set D. Students and teachers of Class 10 Mathematics can get free printable Worksheets for Class 10 Mathematics Chapter 5 Arithmetic Progression in PDF format prepared as per the latest syllabus and examination pattern in your schools. Class 10 students should practice questions and answers given here for Mathematics in Class 10 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 10 Mathematics Worksheets prepared by school teachers as per the latest NCERT, CBSE, KVS books and syllabus issued this academic year and solve important problems with solutions on daily basis to get more score in school exams and tests

## Worksheet for Class 10 Mathematics Chapter 5 Arithmetic Progression

Class 10 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 5 Arithmetic Progression in Class 10. This test paper with questions and answers for Class 10 will be very useful for exams and help you to score good marks

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

ARITHMETIC PROGRESSIONS

Question. Find the sum of the first 22 terms of the AP : 8, 3, –2, . . .

Question. If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
5th term

Question. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Question. How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?
4 or 13

Question. In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will 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 till Class XII. There are three sections of each class. How many trees will be planted by the students?
234

Question. For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
13

Question. lf 2x, x + 10, 3x + 2 are in A.P., find the value of x.
lf 2x, x + 10, 3x + 2 are in A.P.,we have to find the value of x.
Since, 2x, x + 10, 3x + 2 are in A.P.therefore 2 (x + 10) = 2x + 3x + 2
2x + 20 = 5x + 2
3x = 18 x = 6

Question. Find 7th term from the end of the AP : 7, 10 , 13,....,184.
Given, AP is 7, 10 , 13,....,184.
we have to find 7th term from the end reversing the AP , 184,.....,13,10,7.
now, = common difference = 7-10 = -3
7th term from the beginning of AP =a+(7-1)d=a+6d
=184+(6 ×(-3))
= 184 - 18 = 166

Question. Find the 11th term from the end of the AP 10,7,4,....,-62.
a = 10, d = (7-10) = -3, l = -62 and n = 11.
11th term from the end = [l - (n -1) d]
= {-62 - (11 -1)× (-3)}
= (-62 + 30) = -32.
Hence, the 11th term from the end of the given AP is -32.

Question. Divide 24 in three parts such that they are in AP and their product is 440.
Answer : Let the required numbers in A.P.are (a - d), a and (a + d).
Sum of these numbers = (a - d) + a + (a + d) = 3a
Product of these numbers = (a - d)× a × (a + d)=a(a2 - d2)
But given, sum = 24 and product = 440
∴ 3a = 24
a = 8
and a(a2 - d2) = 8(64 - d2) = 440 [ a = 8]
Or, 64 - d2 = 55
Or, d2 = 64 - 55
=> d2 = 9
=> d = ± 3
When a = 8 and d = 3
The required numbers are (5, 8, 11).
When a = 8 and d = -3
The required numbers are ( 11, 8, 5 ).

Question. Determine an A.P. whose third term is 9 and when fifth term is subtracted from 8th term, we get 6.
Answer : Let the first term be a and the common difference be d.
an = a + (n - 1)d
Here given, a3 =9
or, a + 2d = 9 ....(i)
a8 - a5 = 6
or, (a + 7d) - (a + 4d) = 6
a + 7d - a - 4d = 6
or, 3d = 6
or, d = 2 ....(ii)
Substituting this value of d from (ii) in (i), we get
or, a + 2(2) = 9
or, a + 4 = 9
or a = 9 - 4
or, a = 5
a = 5 and d = 2
So, A.P. is 5,7,9,11,....

Question. If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
a9 = 0
a + (9 - 1)d = 0
a + 8d = 0
a = -8d
To prove: a29 = 2a19
Proof: LHS = a29
= a + (29 - 1)d
= a + 28d
= -8d + 28d = 20d
RHS = 2a19
= 2 a + (19 - 1)d]
= 2[ -8d + 18d]
= 2 10d
= 20d
LHS = RHS
Hence, 29th term is double the 19th term.

Question. Find the first four terms of an A.P. whose first term is - 2 and common difference is - 2.
Answer : given a1= -2, common difference d= -2
a1 = -2 ,
a2 = a1 + d = -2 + (-2) = -4
a3 = a2 + d = -4 + ( -2) = -6
a4 = a3 + d = =-6 + (-2) = -8
First four terms are - 2, - 4, - 6, - 8

Question. If the sum of n terms of an A.P. is 2n2 + 5n, then find the 4th term.
Answer : Let the sum of n terms of A.P. = Sn.
Given, Sn = 2n2 + 5n
Now, nth term of A.P, = Sn - Sn-1
or, an = (2n2 + 5n) - [2(n - 1)2 + 5 (n - 1)]
an= (2n2 + 5n) - [2(n2 -2n + 1) + 5 (n - 1)]
an = 2n2 + 5n - [2n2 - 4n + 2 + 5n - 5]
an = 2n2 + 5n - [2n2+ n - 3]
an = 2n2 + 5n - 2n2 - n + 3
an = 4n + 3
4th term a4=4×4+3
=16+3=19

Question. In the following AP's find the missing terms: 2, __, 26.
We know that the difference between consecutive terms is equal in any A.P.
Let the missing term be x .
x - 2 = 26 - x ⇒ 2x = 28 ⇒ x = 14
Therefore, missing term is 14.

More question-

1. S17 − S16 = ?

(a) S1

(b) T1

(c) T17

(d) 2d

2. T10 of an AP = 31 & T20 = 71 then T30 = ?

(a) 171

(b) 222

(c) 112

(d) 111

3. No. of terms of the sequence −12, −9, −6, −3, …….. must be added to make the sum 54 are _____

(a) 33

(b) −46

(d) 10

(d) 12

4. If ‘n’ times the ‘n’th term an AP is equal to m times its ‘m’th term, then (m + n)th term is _____

(a) 0

(b) 1

(c) −1

(d) 2

5. The sum of three numbers in an AP is (−3), and their product is 8. Then numbers are

(a) −4, −1, 2

(b) −4, −1, −2

(c) 4, 1, 2

(d) 2, 1, −4

6. The sum of four numbers is 20 and sum of whose squares is 120. This nos. are _____

(a) 2, 4, −6, −8

(b) 2, 4, 6, 8

(c) 8, 6, 2, −1

(d) 8, 6, −2, 1

7. The nth term of a pattern of numbers is 2n + 1. The common difference of this AP is ________.

(a) 2

(b) −2

(c) 3

(d) −3

8. Which term of the AP 3, 8, 13, 18………… is 78 ?

(a) t15

(b) t16

(c) t17

(d) t18

9. Which term of the sequence 114, 109, 104, ………….. is the first negative term ?

(a) t23

(b) t24

(c) t25

(d) None of these

10. The sum of first 18 terms of an AP whose nth term is 3 − 2n is

(a) −288

(b) 250

(c) −278

(d) −260

11. If 2x, x + 10, 3x + 2 are in AP, then the value of x is

(a) 6

(b) 5

(c) 4

(d) 3

12. The 9th term of an AP is 499 and 499th term is 9. The term which is equal to zero is

(a) t508

(b) t805

(c) t504

(d) t501

13. If in an AP a = 1, tn = 20 and Sn = 399 then n is

(a) 19

(b) 21

(c) 38

(d) 42

14. Two APs have the same common difference. The first term of one of these −1 and that of the other is −8. Then the difference between their 4th term is

(a) −1

(b) −8

(c) 7

(d) −9

15. Sum of n terms of the series ..........321882++++ is

(a) ()21+nn

(b) ()312+nn

(c) ()21+nn

(d) None of these

16. The sum of first 50 odd natural numbers is

(a) 2500

(b) 2400

(c) 2600

(d) 2300

17. If nnnnbaba++++11 is the AM between a and b, then the value of n is

(a) 1

(b) −1

(c) 0

(d) None of these

18. If an AP a = −2.5, d = 0.5, an = 7.5 then n is

(a) 20

(b) 21

(c) 3.6

(d) −3.6

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