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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 813 · 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 the first 7 terms of the AP 1, 6, 11, …? (a) 117 (b) 224 (c) 31 (d) 112
  2. 2.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 20 (b) 18 (c) 19 (d) 17
  3. 3.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 154 (b) 20 (c) 77 (d) 80
  4. 4.Which term of the AP 7, 12, 17, 22, … is 137? (a) 29th (b) 27th (c) 28th (d) 26th
  5. 5.What is the 21st term of the AP 19, 21, 23, 25, …? (a) 59 (b) 42 (c) 61 (d) 40
  6. 6.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 22 (b) 17 (c) 15 (d) 16
  7. 7.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 231 (b) 220 (c) 440 (d) 30
  8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 49 (d) 28
  9. 9.What is the 39th term of the AP 8, 17, 26, 35, …? (a) 350 (b) 351 (c) 342 (d) 359
  10. 10.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 406 (d) 784
  11. 11.What is the 28th term of the AP 14, 21, 28, 35, …? (a) 189 (b) 196 (c) 210 (d) 203
  12. 12.What is the 16th term of the AP 13, 19, 25, 31, …? (a) 109 (b) 103 (c) 90 (d) 96
  13. 13.Which term of the AP 3, 5, 7, 9, … is 75? (a) 39th (b) 38th (c) 37th (d) 36th
  14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 21 (d) 11
  15. 15.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 200 (b) 352 (c) 43 (d) 176
  16. 16.What is the 16th term of the AP 20, 29, 38, 47, …? (a) 144 (b) 135 (c) 164 (d) 155
  17. 17.What is the 30th term of the AP 14, 18, 22, 26, …? (a) 134 (b) 130 (c) 120 (d) 116
  18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  19. 19.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 52 (b) 56 (c) 104 (d) 10
  20. 20.What is the 33rd term of the AP 16, 18, 20, 22, …? (a) 66 (b) 82 (c) 80 (d) 64
  21. 21.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 166 (b) 20 (c) 165 (d) 330
  22. 22.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 43 (d) 506
  23. 23.What is the 22nd term of the AP 11, 15, 19, 23, …? (a) 95 (b) 88 (c) 99 (d) 84
  24. 24.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 192 (b) 176 (c) 36 (d) 352
  25. 25.What is the 23rd term of the AP 8, 12, 16, 20, …? (a) 88 (b) 96 (c) 92 (d) 100
  26. 26.Which term of the AP 16, 21, 26, 31, … is 161? (a) 30th (b) 32nd (c) 29th (d) 31st
  27. 27.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 44 (b) 264 (c) 286 (d) 528
  28. 28.What is the 23rd term of the AP 6, 8, 10, 12, …? (a) 52 (b) 50 (c) 46 (d) 44
  29. 29.What is the 11th term of the AP 16, 25, 34, 43, …? (a) 106 (b) 115 (c) 99 (d) 90
  30. 30.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 230 (b) 215 (c) 35 (d) 430
  31. 31.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 11 (c) 70 (d) 35
  32. 32.Which term of the AP 19, 27, 35, 43, … is 299? (a) 38th (b) 35th (c) 36th (d) 37th
  33. 33.What is the missing term in the AP 19, 24, ?, 34, 39? (a) 34 (b) 30 (c) 28 (d) 29
  34. 34.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 49 (b) 56 (c) 13 (d) 98
  35. 35.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 24 (b) 22 (c) 21 (d) 20
  36. 36.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 540 (b) 1008 (c) 75 (d) 504
  37. 37.What is the missing term in the AP 11, 13, 15, ?, 19? (a) 19 (b) 18 (c) 17 (d) 16
  38. 38.What is the 24th term of the AP 1, 4, 7, 10, …? (a) 70 (b) 73 (c) 69 (d) 72
  39. 39.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 351 (d) 676
  40. 40.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 9 (b) 14 (c) 8 (d) 7

Answer key

  1. 112
  2. 18
  3. 77
  4. 27th
  5. 59
  6. 16
  7. 220
  8. 49
  9. 350
  10. 784
  11. 203
  12. 103
  13. 37th
  14. 36
  15. 176
  16. 155
  17. 130
  18. 289
  19. 52
  20. 80
  21. 165
  22. 484
  23. 95
  24. 176
  25. 96
  26. 30th
  27. 264
  28. 50
  29. 106
  30. 215
  31. 35
  32. 36th
  33. 29
  34. 49
  35. 21
  36. 504
  37. 17
  38. 70
  39. 676
  40. 8

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