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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 106 · 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 75? (a) 2775 (b) 2850 (c) 2851 (d) 5700
  2. 2.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  3. 3.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4095 (c) 8372 (d) 4186
  4. 4.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 30 (b) 31 (c) 38 (d) 29
  5. 5.What is the 39th term of the AP 12, 15, 18, 21, …? (a) 114 (b) 117 (c) 129 (d) 126
  6. 6.What is the 11th term of the AP 13, 18, 23, 28, …? (a) 55 (b) 68 (c) 50 (d) 63
  7. 7.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 325 (c) 650 (d) 49
  8. 8.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 60 (b) 10 (c) 55 (d) 110
  9. 9.What is the 27th term of the AP 19, 25, 31, 37, …? (a) 175 (b) 156 (c) 162 (d) 181
  10. 10.What is the 37th term of the AP 12, 14, 16, 18, …? (a) 72 (b) 84 (c) 74 (d) 86
  11. 11.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 25 (b) 15 (c) 16 (d) 17
  12. 12.What is the 34th term of the AP 20, 29, 38, 47, …? (a) 326 (b) 317 (c) 306 (d) 297
  13. 13.What is the 23rd term of the AP 2, 7, 12, 17, …? (a) 117 (b) 110 (c) 112 (d) 115
  14. 14.Which term of the AP 17, 19, 21, 23, … is 33? (a) 9th (b) 11th (c) 10th (d) 8th
  15. 15.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 12 (b) 20 (c) 13 (d) 14
  16. 16.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  17. 17.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 32 (b) 25 (c) 23 (d) 24
  18. 18.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 105 (c) 120 (d) 121
  19. 19.What is the 28th term of the AP 7, 16, 25, 34, …? (a) 259 (b) 250 (c) 252 (d) 243
  20. 20.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 14 (b) 15 (c) 13 (d) 21
  21. 21.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 18 (b) 19 (c) 20 (d) 17
  22. 22.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 23 (b) 25 (c) 29 (d) 24
  23. 23.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 78 (b) 15 (c) 150 (d) 75
  24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  25. 25.What is the missing term in the AP 11, 18, 25, ?, 39? (a) 33 (b) 31 (c) 32 (d) 39
  26. 26.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 4 (c) 3 (d) 5
  27. 27.What is the 32nd term of the AP 4, 13, 22, 31, …? (a) 279 (b) 292 (c) 283 (d) 288
  28. 28.What is the 28th term of the AP 19, 22, 25, 28, …? (a) 100 (b) 103 (c) 81 (d) 84
  29. 29.Which term of the AP 6, 10, 14, 18, … is 78? (a) 21st (b) 19th (c) 20th (d) 18th
  30. 30.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 24 (b) 198 (c) 99 (d) 108
  31. 31.What is the 37th term of the AP 17, 19, 21, 23, …? (a) 91 (b) 74 (c) 89 (d) 72
  32. 32.Which term of the AP 8, 13, 18, 23, … is 183? (a) 37th (b) 36th (c) 38th (d) 35th
  33. 33.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4851 (c) 9900 (d) 4950
  34. 34.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 322 (b) 182 (c) 41 (d) 161
  35. 35.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  36. 36.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
  37. 37.What is the 29th term of the AP 12, 20, 28, 36, …? (a) 236 (b) 244 (c) 232 (d) 224
  38. 38.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 260 (b) 140 (c) 22 (d) 130
  39. 39.What is the 22nd term of the AP 8, 10, 12, 14, …? (a) 44 (b) 42 (c) 50 (d) 52
  40. 40.What is the missing term in the AP 16, 24, ?, 40, 48? (a) 40 (b) 31 (c) 32 (d) 33

Answer key

  1. 2850
  2. 121
  3. 4186
  4. 30
  5. 126
  6. 63
  7. 625
  8. 55
  9. 175
  10. 84
  11. 16
  12. 317
  13. 112
  14. 9th
  15. 13
  16. 49
  17. 24
  18. 120
  19. 250
  20. 14
  21. 18
  22. 24
  23. 75
  24. 81
  25. 32
  26. 4
  27. 283
  28. 100
  29. 19th
  30. 99
  31. 89
  32. 36th
  33. 4950
  34. 161
  35. 729
  36. 900
  37. 236
  38. 130
  39. 50
  40. 32

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