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Study Material for Class 10 Mathematics Chapter 5 Arithmetic Progression
Class 10 Mathematics students should refer to the following Pdf for Chapter 5 Arithmetic Progression in Class 10. These notes and test paper with questions and answers for Class 10 Mathematics will be very useful for exams and help you to score good marks
Class 10 Mathematics Chapter 5 Arithmetic Progression
CBSE Class 10 Arithmetic Progressions Sure Shot Questions Set B. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations. Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.
1. Find the sum of first 24 terms of the AP 5, 8, 11, 14,…….
2. Find the sum: 25 + 28 + 31 +……….. + 100.
3. Find the sum of first 21 terms of the AP whose 2nd term is 8 and 4th term is 14.
4. If the nth term of an AP is (2n + 1), find the sum of first n terms of the AP.
5. Find the sum of first 25 terms of an AP whose nth term is given by (7 – 3n).
6. Find the sum of all two-digit odd positive numbers.
7. Find the sum of all natural number between 100 and 500 which are divisible by 8.
8. Find the sum of all three digit natural numbers which are multiples of 7.
9. How many terms of the AP 3, 5, 7, 9,… must be added to get the sum 120?
10. If the sum of first n, 2n and 3n terms of an AP be S1, S2 and S3 respectively, then prove that S3 =3(S2 – S1).
11. If the sum of the first m terms of an AP be n and the sum of first n terms be m then show that the sum of its first (m + n) terms is –(m + n).
12. If the sum of the first p terms of an AP is the same as the sum of first q terms (where p ≠q) then show that the sum of its first (p + q) terms is 0.
13. If the pth term of an AP is 1/q and its qth term is 1/ p, show that the sum of its first pq terms is1/2( p +q) .
14. Find the sum of all natural numbers less than 100 which are divisible by 6.
15. Find the sum of all natural number between 100 and 500 which are divisible by 7.
16. Find the sum of all multiples of 9 lying between 300 and 700.
17. Find the sum of all three digit natural numbers which are divisible by 13.
18. Find the sum of 51 terms of the AP whose second term is 2 and the 4th term is 8.
19. The sum of n terms of an AP is (5n2 – 3n). Find the AP and hence find its 10th term.
21. If the sum of first 7 terms of AP is 49 and that of first 17 terms is 289, find the sum of first n terms.
22. Find the sum of the first 100 even natural numbers which are divisible by 5.
23. Find the sum of the following: -1-1/n) +(1-2/n) +(1-3/n)........upto n terms.
24. If the 5th and 12th terms of an AP are – 4 and – 18 respectively, find the sum of first 20 terms of the AP.
25. The sum of n terms of an AP is (5n2/2 + 3n/2) Find its 20th term.
26. The sum of n terms of an AP is (3n2 /2 5n) . Find its 25th term
27. Find the number of terms of the AP 18, 15, 12, ……. so that their sum is 45. Explain the double answer.
28. Find the number of terms of the AP 64, 60, 56, ……. so that their sum is 544. Explain the double answer.
29. Find the number of terms of the AP 17, 15, 13, ……. so that their sum is 72. Explain the double answer.
30. Find the number of terms of the AP 63, 60, 57, ……. so that their sum is 693. Explain the double answer.
31. The sum of first 9 terms of an AP is 81 and the sum of its first 20 terms is 400. Find the first term and the common difference of the AP.
32. If the nth term of an AP is (4n + 1), find the sum of the first 15 terms of this AP. Also find the sum of is n terms.
33. The sum of the first n terms of an AP is given by Sn = (2n2 + 5n). Find the nth term of the AP.
34. If the sum of the first n terms of an AP is given by Sn = (3n2 – n), find its 20th term.
35. If the sum of the first n terms of an AP is given by Sn = (3n2 + 2n), find its 25th term.
36. How many terms of the AP 21, 18, 15,…. Must be added to get the sum 0?
37. Find the sum of first 24 terms whose nth term is given by an = 3 + 2n.
38. How many terms of the AP –6, 11 /2 , –5, ……. are needed to give the sum -25? Explain the double answer.
40. How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?
41. Find the sum of the first 40 positive integers divisible by 6.
42. Find the sum of all the two digit numbers which are divisible by 4.
43. Find the sum of all two digits natural numbers greater than 50 which, when divided by 7 leave remainder of 4.
44. 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
45. If the sum of first n terms of an A.P. is given by Sn = 3n2 + 5n, find the nth term of the A.P.
46. The sum of first 8 terms of an AP is 100 and the sum of its first 19 terms is 551. Find the AP.
47. How many terms are there in A.P. whose first terms and 6th term are –12 and 8 respectively and sum of all its terms is 120?
48. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row,18 in the row next to it and so on. In how may rows are the 200 logs placed and how many logs are in the top row?
49. A man repays a loan of Rs. 3250 by paying Rs. 20 in the first month and then increase the payment by Rs. 15 every month. How long will it take him to clear the loan?
50. Raghav buys a shop for Rs. 1,20,000. He pays half of the amount in cash and agrees to pay the balance in 12 annual installments of Rs. 5000 each. If the rate of interest is 12% and he pays with the installment the interest due on the unpaid amount, find the total cost of the shop.
51. A sum of Rs. 280 is to be used to give four cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.
52. A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
53. A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day, etc., the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
54. A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year.
Assuming that the production increases uniformly by a fixed number every year, find : (i) the production in the 1st year (ii) the production in the 10th year (iii) the total production in first 7 years.
55. How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
56. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
58. Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
59. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
60. 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.
61. Show that a1, a2, . . ., an, . . . form an AP where an is defined as below : (i) an = 3 + 4n
(ii) an = 9 – 5n Also find the sum of the first 15 terms in each case.
62. If the sum of the first n terms of an AP is 4n – n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.
63. Find the sum of the first 15 multiples of 8.
64. Find the sum of the odd numbers between 0 and 50.
65. 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?
66. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . .. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take Π = 22/7)
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CBSE Class 10 Mathematics Chapter 5 Arithmetic Progression Study Material
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Study Material for Mathematics CBSE Class 10 Chapter 5 Arithmetic Progression
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