Class 10th A.P.

Class 10th A.P.

Arithmetic Progressions

Que1. Which term of the A.P. 3, 8, 13…… is 248?

Que2. Which term of the A.P. 84, 80, 76……….is 0?

Que3. Which term of the A.P. 4, 9, 14 ………. is 254?

Que4. Which term of the A.P. 21, 42, 63, 84………… is 420?

Que5. Which term of the A.P.  121, 117, 113, ………….is its first negative term?

Que6. Is 68 a term of the A.P. 7, 10, 13…….. ?

Que7. Is 302 a term of the A.P. 3, 8, 13,…….?

Que8. Is -150 a term of the A.P.  11,8,,5,2……?

Que9. The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.

Que10. The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

Que11. If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.

Que12. If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.

Que13. The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.

Que14.Q15. In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.

Que15.Q16. The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.

Que16.Q17. Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.

Que17.Q18. How many numbers of two digit are divisible by 3?

Que18.Q19. An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.

Que19.Q20. The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.?

Que20.Q21. The first term of an A.P. is 5 and its 100th term is - 292. Find the 50th term of this A.P.

Que21.Q22. Find the arithmetic progression whose third term is 16 and seventh term exceeds its fifth term by 12.

Que22.Q23. The 7th term of an A.P. is 32 and its 13th term is 62. Find the A.P.        

Que23.Q24. Which term of the A.P. 3, 10, 17……… will be 84 more than its 13th term?

Que24.Q25. How many multiples of 4 lie between 10 and 250?

Que25.Q26. How many three digit numbers are divisible by 7?

Que26.Q27. Which term of the arithmetic progression 8, 14, 20, 26……. will be72 more than its 41th term?

Que27.Q28. Find the term of the arithmetic progression 9, 12, 15, 18……..which is 39 more than its 36th term.

Que28.Q29. Find the 8th term from the end of the A.P. 7, 10, 13………..,184.

Que29.Q30. Find the 10th term from the end of the A.P. 8, 10, 12, ..., 126

Que30.Q31. The sum of 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the A.P.

Que31.Q32. Which term of the A.P. 3, 15, 27, 39……….will be 120 more than its 21st term?

Que32.Q33. The 17th term of an A.P. is 5 more than twice its 8th term. If the 11th term of the A.P. is 43, find the nth term.

Que33.Q34. Find the number of all three digit natural numbers which are divisible by 9.

Que34.Q35. The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.

Que35.Q36. The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.

Que36.Q37. The 24th term of an A.P. is twice its 10th term. Show that its 72nd term is 4 times its 15th term.

Que37.Q38. Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

Que38.Q39. If the seventh term of an A.P. is 1/9 and its ninth term is 1/7, find its (63)rd term.

Que39.Q40. The sum of 5th and 9th terms of an AP is 30. If its 25th term is three times its 8th term, find the AP.

Que40.Q41. Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31………

Que41.Q42. Find the middle term of the A.P. 213, 205, 197………..,37.

Que42.Q43. If the 5th term of an A.P. is 31 and 25th term is 140 more than the 5th term, find the A.P.

Que43. Find the sum of the first:

a.                        11 terms of the A.P : 2, 6, 10, 14……

b.                        13 terms of the A.P : -6, 0, 6, 12.……

c.                         51 terms of the A.P. whose second term is 2 and fourth term is 8.

Que44. The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds these term by 6, find three terms.

Que45. Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.

Que46. Find the four numbers in A.P. whose sum is 50 and in which the greatest number is 4 times the least.

Que47. The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.

Que48. Find the value of x for which (8x + 4), (6x – 2), (2x + 7) are in A.P.

Que49. If x + 1, 3x and 4x + 2 are in A.P, find the value of x.

Que50. Show that (a–b)2, (a2+b2) and (a + b)2 are in A.P.

Q51. Find the sum on n term of the A.P.  5, 2, -1, -4, -7…..

Q52. If the n sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19 ……. is 116. Find the last term.

Q53. How many terms of the sequence  18, 16, 14…….should be taken so that their sum is zero?

Q54. How many terms are there in the A.P. whose first and fifth terms are 14 and 2 respectively and the sum of the terms is 40?

Q55. How many terms of the A.P. 9, 17, 25…….. must be taken so that their sum is 636?

Q56. How many terms of the A.P. 63, 60, 57…….. must be taken so that their sum is 693?

Q57. The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Q58. The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.

Q60.The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

Q61. If 12th term of an A.P. is 13 and the sum of the first four terms is 24, what is the sum of first 10 terms?

Q62. Find the sum of first 22 terms of an A.P. in which d = 22 and a22 = 149.

Q63. Find the sum of all natural numbers between a and 100, which are divisible by 3.

Q64.Find the sum of all odd numbers between

i.                 0 and 50

ii.               100 and 200

Q65. The nth term of an A.P. is 6n+2. Find the common difference

Q66. Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.

Q67. Find the sum of all integers between 84 and 719, which are multiples of 5.

Q68. Find the sum of all integers between 50 and 500, which are multiples of 7.

Q69. Find the sum of all even integers between 101 and 999.

Q70. Find the sum of all integers between 100 and 550, which are multiples of 9.

Q71. In an A.P. if the first term is 22, the common difference is – 4 and the sum to n terms is 64, find n.

Q72. In an A.P. If the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?

Q73. Find the sum of :

a)     The first 15 multiples of 8

b)     The first 40 positive integers divisible by (a) 3 (b) 5 (c) 6.

               

 

c)     All 3 – digit natural numbers which are divisible by 13.

d)     All 3 – digit natural numbers, which are multiples of 11.

Q74. Find the sum of the first 25 terms of an A.P. whose nth term is given by a_n = 7 – 3n.

Q75. Find the sum of the first 25 terms of an A.P. whose second and third terms are 14 and 18 respectively.

Q76. If the sum of 7 terms of an A.P. is 49 and that of 17 term is 289, find the sum of n terms.

Q77. The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Q78. Aman saved Rs. 16500 in ten years. In each year after the first he saved Rs.100 more than he did in the preceding year. How much did he save in the first year?

Q79. Aman saved Rs.32 during the first year, Rs.36 in the second year and in this way he increases his savings by Rs.4 every year. Find in what time his saving will be Rs.200.

Q80. Aman arrange stop ay off a debt of Rs.3600 by 40 annual installments which for man arithmetic series. When 30 of the installments are paid, he dies leaving one - third of the debt unpaid, find the value of the first installment.

Q81. There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and here turns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.

Q82. A man is employed to count Rs.10710. He counts at there of Rs.180 per minute for half an hour. After this, he counts at the rate of Rs.3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.

Q83. A piece of equipment cost a certain factory Rs.600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and soon. What will be its value at the end of 10 years, all percentages applying to the original cost?

Q84. A sum of Rs.700 is to be used to gives even 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 prize.

Q85. In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.

Q86. In an A.P., the first term is 22, nth term is -11 and the sum to first n terms is 66. Find n and d, the common difference.

Q87. The first and the last term of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?