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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 493 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 666 (c) 630 (d) 1332
  2. 2.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 154 (d) 136
  3. 3.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2145 (c) 2178 (d) 2211
  4. 4.Which term of the AP 6, 11, 16, 21, … is 151? (a) 29th (b) 31st (c) 32nd (d) 30th
  5. 5.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 33 (b) 27 (c) 25 (d) 26
  6. 6.What is the sum of all the whole numbers from 1 to 39? (a) 1560 (b) 780 (c) 741 (d) 781
  7. 7.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 11 (b) 12 (c) 10 (d) 13
  8. 8.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 50 (c) 110 (d) 55
  9. 9.Which term of the AP 5, 14, 23, 32, … is 77? (a) 9th (b) 10th (c) 11th (d) 8th
  10. 10.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 95 (b) 80 (c) 28 (d) 160
  11. 11.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 17 (b) 19 (c) 15 (d) 16
  12. 12.What is the 16th term of the AP 6, 12, 18, 24, …? (a) 90 (b) 102 (c) 97 (d) 96
  13. 13.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 264 (b) 480 (c) 240 (d) 51
  14. 14.What is the 20th term of the AP 3, 12, 21, 30, …? (a) 180 (b) 174 (c) 171 (d) 183
  15. 15.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 26 (b) 180 (c) 90 (d) 100
  16. 16.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 4950 (c) 4951 (d) 9900
  17. 17.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 841 (d) 57
  18. 18.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 15 (b) 19 (c) 13 (d) 14
  19. 19.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 43 (b) 636 (c) 318 (d) 336
  20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 90 (d) 45
  21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 25 (d) 30
  22. 22.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 187 (b) 352 (c) 26 (d) 176
  23. 23.Which term of the AP 8, 17, 26, 35, … is 161? (a) 19th (b) 18th (c) 20th (d) 17th
  24. 24.What is the 12th term of the AP 6, 15, 24, 33, …? (a) 108 (b) 114 (c) 99 (d) 105
  25. 25.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 135 (b) 27 (c) 270 (d) 138
  26. 26.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 38 (b) 140 (c) 161 (d) 280
  27. 27.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 1892 (c) 903 (d) 946
  28. 28.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 160 (b) 80 (c) 26 (d) 85
  29. 29.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 480 (b) 73 (c) 516 (d) 960
  30. 30.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 160 (c) 300 (d) 150
  31. 31.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 54 (b) 10 (c) 108 (d) 55
  32. 32.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 34 (b) 37 (c) 30 (d) 27
  33. 33.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 190 (c) 380 (d) 171
  34. 34.Which term of the AP 9, 16, 23, 30, … is 135? (a) 19th (b) 20th (c) 18th (d) 21st
  35. 35.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 264 (b) 242 (c) 484 (d) 42
  36. 36.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 15 (b) 14 (c) 16 (d) 21
  37. 37.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 2346 (c) 2416 (d) 4830
  38. 38.What is the 11th term of the AP 3, 7, 11, 15, …? (a) 44 (b) 43 (c) 40 (d) 47
  39. 39.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 351 (d) 702
  40. 40.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 408 (c) 816 (d) 444

Answer key

  1. 666
  2. 153
  3. 2211
  4. 30th
  5. 26
  6. 780
  7. 11
  8. 55
  9. 9th
  10. 80
  11. 16
  12. 96
  13. 240
  14. 174
  15. 90
  16. 4950
  17. 841
  18. 14
  19. 318
  20. 81
  21. 25
  22. 176
  23. 18th
  24. 105
  25. 135
  26. 140
  27. 946
  28. 80
  29. 480
  30. 150
  31. 54
  32. 34
  33. 190
  34. 19th
  35. 242
  36. 15
  37. 2415
  38. 43
  39. 676
  40. 408

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