CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set D

ARITHMETIC PROGRESSIONS

Very Short Answer type Questions

Question. Find the sum of the first 22 terms of the AP : 8, 3, –2, . . .
Answer : – 979

Question. If the 3^rd and the 9^th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Answer : 5^th 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.
Answer : n²

Question. How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?
Answer : 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?
Answer : 234

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

Short Answer type Questions

Question. lf 2x, x + 10, 3x + 2 are in A.P., find the value of x.
Answer : 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. 
Answer : 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

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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