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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 288 · 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 29? (a) 406 (b) 435 (c) 436 (d) 870
  2. 2.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  3. 3.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 63 (b) 126 (c) 11 (d) 64
  4. 4.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  5. 5.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 25 (b) 7 (c) 50 (d) 26
  6. 6.What is the 15th term of the AP 15, 18, 21, 24, …? (a) 42 (b) 60 (c) 57 (d) 45
  7. 7.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 84 (b) 21 (c) 87 (d) 168
  8. 8.What is the 15th term of the AP 12, 15, 18, 21, …? (a) 42 (b) 45 (c) 54 (d) 57
  9. 9.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 900 (d) 930
  10. 10.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 60 (b) 108 (c) 54 (d) 14
  11. 11.What is the 10th term of the AP 12, 20, 28, 36, …? (a) 92 (b) 80 (c) 72 (d) 84
  12. 12.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 10 (b) 12 (c) 9 (d) 11
  13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  14. 14.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 60 (b) 360 (c) 660 (d) 330
  15. 15.What is the 12th term of the AP 16, 21, 26, 31, …? (a) 71 (b) 60 (c) 55 (d) 76
  16. 16.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 60 (b) 18 (c) 100 (d) 50
  17. 17.What is the 14th term of the AP 3, 11, 19, 27, …? (a) 107 (b) 115 (c) 112 (d) 104
  18. 18.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 330 (c) 300 (d) 600
  19. 19.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 630 (c) 648 (d) 1332
  20. 20.What is the 23rd term of the AP 14, 22, 30, 38, …? (a) 190 (b) 184 (c) 176 (d) 198
  21. 21.Which term of the AP 11, 13, 15, 17, … is 73? (a) 31st (b) 32nd (c) 34th (d) 33rd
  22. 22.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 208 (b) 20 (c) 104 (d) 112
  23. 23.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 190 (b) 360 (c) 27 (d) 180
  24. 24.What is the 29th term of the AP 10, 13, 16, 19, …? (a) 94 (b) 87 (c) 84 (d) 97
  25. 25.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1770 (c) 1711 (d) 1771
  26. 26.What is the 36th term of the AP 5, 14, 23, 32, …? (a) 320 (b) 315 (c) 324 (d) 329
  27. 27.What is the 29th term of the AP 14, 23, 32, 41, …? (a) 275 (b) 266 (c) 261 (d) 252
  28. 28.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 153 (c) 342 (d) 171
  29. 29.Which term of the AP 11, 18, 25, 32, … is 109? (a) 14th (b) 16th (c) 17th (d) 15th
  30. 30.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 32 (b) 39 (c) 31 (d) 30
  31. 31.What is the 22nd term of the AP 19, 25, 31, 37, …? (a) 145 (b) 151 (c) 126 (d) 132
  32. 32.Which term of the AP 18, 21, 24, 27, … is 57? (a) 19th (b) 13th (c) 14th (d) 15th
  33. 33.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 8742 (c) 4278 (d) 4371
  34. 34.Which term of the AP 2, 9, 16, 23, … is 184? (a) 27th (b) 26th (c) 28th (d) 29th
  35. 35.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 27 (b) 26 (c) 25 (d) 32
  36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 110 (d) 100
  37. 37.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 13 (b) 10 (c) 11 (d) 9
  38. 38.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 8 (c) 35 (d) 70
  39. 39.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 26 (b) 192 (c) 108 (d) 96
  40. 40.What is the 14th term of the AP 18, 27, 36, 45, …? (a) 126 (b) 117 (c) 135 (d) 144

Answer key

  1. 435
  2. 576
  3. 63
  4. 289
  5. 25
  6. 57
  7. 84
  8. 54
  9. 900
  10. 54
  11. 84
  12. 10
  13. 25
  14. 330
  15. 71
  16. 50
  17. 107
  18. 300
  19. 666
  20. 190
  21. 32nd
  22. 104
  23. 180
  24. 94
  25. 1770
  26. 320
  27. 266
  28. 171
  29. 15th
  30. 31
  31. 145
  32. 14th
  33. 4371
  34. 27th
  35. 26
  36. 100
  37. 10
  38. 35
  39. 96
  40. 135

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