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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 210 · 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 22nd term of the AP 6, 10, 14, 18, …? (a) 88 (b) 84 (c) 94 (d) 90
  2. 2.Which term of the AP 5, 9, 13, 17, … is 33? (a) 7th (b) 9th (c) 10th (d) 8th
  3. 3.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 28 (b) 27 (c) 35 (d) 26
  4. 4.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 88 (b) 168 (c) 14 (d) 84
  5. 5.What is the 34th term of the AP 12, 18, 24, 30, …? (a) 210 (b) 198 (c) 204 (d) 216
  6. 6.What is the 34th term of the AP 11, 16, 21, 26, …? (a) 176 (b) 170 (c) 165 (d) 181
  7. 7.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 96 (b) 92 (c) 15 (d) 184
  8. 8.What is the 16th term of the AP 8, 17, 26, 35, …? (a) 143 (b) 152 (c) 144 (d) 135
  9. 9.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 11 (b) 36 (c) 72 (d) 42
  10. 10.What is the 40th term of the AP 7, 9, 11, 13, …? (a) 85 (b) 80 (c) 87 (d) 78
  11. 11.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 3916 (c) 4005 (d) 4006
  12. 12.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 528 (c) 1056 (d) 496
  13. 13.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 4951 (c) 4950 (d) 9900
  14. 14.What is the 18th term of the AP 5, 8, 11, 14, …? (a) 56 (b) 51 (c) 54 (d) 59
  15. 15.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 812 (d) 406
  16. 16.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 400 (b) 740 (c) 370 (d) 64
  17. 17.What is the 36th term of the AP 11, 14, 17, 20, …? (a) 116 (b) 119 (c) 105 (d) 108
  18. 18.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 12 (b) 11 (c) 19 (d) 10
  19. 19.What is the 21st term of the AP 14, 17, 20, 23, …? (a) 77 (b) 60 (c) 63 (d) 74
  20. 20.What is the 11th term of the AP 19, 23, 27, 31, …? (a) 44 (b) 59 (c) 40 (d) 63
  21. 21.What is the missing term in the AP 19, 25, 31, ?, 43? (a) 37 (b) 36 (c) 43 (d) 38
  22. 22.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 39 (b) 31 (c) 30 (d) 32
  23. 23.What is the 12th term of the AP 19, 25, 31, 37, …? (a) 66 (b) 72 (c) 91 (d) 85
  24. 24.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 812 (c) 378 (d) 406
  25. 25.What is the 36th term of the AP 12, 15, 18, 21, …? (a) 117 (b) 105 (c) 120 (d) 108
  26. 26.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 992 (d) 496
  27. 27.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 41 (b) 312 (c) 294 (d) 588
  28. 28.What is the missing term in the AP 18, 25, ?, 39, 46? (a) 31 (b) 32 (c) 39 (d) 33
  29. 29.What is the 33rd term of the AP 18, 24, 30, 36, …? (a) 216 (b) 198 (c) 192 (d) 210
  30. 30.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 96 (b) 26 (c) 81 (d) 162
  31. 31.What is the missing term in the AP 16, 25, ?, 43, 52? (a) 33 (b) 43 (c) 35 (d) 34
  32. 32.Which term of the AP 6, 14, 22, 30, … is 102? (a) 14th (b) 15th (c) 12th (d) 13th
  33. 33.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 34 (b) 110 (c) 125 (d) 220
  34. 34.What is the 28th term of the AP 12, 16, 20, 24, …? (a) 108 (b) 112 (c) 124 (d) 120
  35. 35.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 256 (c) 31 (d) 136
  36. 36.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 61 (b) 120 (c) 60 (d) 14
  37. 37.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 153 (c) 306 (d) 136
  38. 38.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 34 (b) 320 (c) 160 (d) 176
  39. 39.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 138 (b) 276 (c) 38 (d) 156
  40. 40.What is the 12th term of the AP 4, 8, 12, 16, …? (a) 48 (b) 49 (c) 44 (d) 52

Answer key

  1. 90
  2. 8th
  3. 27
  4. 84
  5. 210
  6. 176
  7. 92
  8. 143
  9. 36
  10. 85
  11. 4005
  12. 528
  13. 4950
  14. 56
  15. 784
  16. 370
  17. 116
  18. 11
  19. 74
  20. 59
  21. 37
  22. 31
  23. 85
  24. 406
  25. 117
  26. 496
  27. 294
  28. 32
  29. 210
  30. 81
  31. 34
  32. 13th
  33. 110
  34. 120
  35. 256
  36. 60
  37. 153
  38. 160
  39. 138
  40. 48

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