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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 422 · 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 73? (a) 2702 (b) 5402 (c) 2628 (d) 2701
  2. 2.What is the 32nd term of the AP 9, 11, 13, 15, …? (a) 71 (b) 64 (c) 62 (d) 73
  3. 3.What is the 23rd term of the AP 4, 9, 14, 19, …? (a) 114 (b) 115 (c) 119 (d) 110
  4. 4.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 29 (b) 37 (c) 28 (d) 30
  5. 5.What is the 20th term of the AP 20, 23, 26, 29, …? (a) 80 (b) 60 (c) 57 (d) 77
  6. 6.Which term of the AP 6, 15, 24, 33, … is 168? (a) 19th (b) 18th (c) 20th (d) 21st
  7. 7.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 2278 (d) 4556
  8. 8.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 2775 (c) 5550 (d) 2701
  9. 9.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 55 (d) 19
  10. 10.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 30 (b) 105 (c) 200 (d) 100
  11. 11.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 372 (b) 21 (c) 192 (d) 186
  12. 12.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 379 (c) 378 (d) 351
  13. 13.What is the 12th term of the AP 6, 13, 20, 27, …? (a) 77 (b) 84 (c) 90 (d) 83
  14. 14.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 40 (b) 48 (c) 38 (d) 39
  15. 15.Which term of the AP 7, 15, 23, 31, … is 223? (a) 27th (b) 30th (c) 28th (d) 29th
  16. 16.What is the 24th term of the AP 7, 13, 19, 25, …? (a) 144 (b) 138 (c) 151 (d) 145
  17. 17.What is the 37th term of the AP 8, 15, 22, 29, …? (a) 267 (b) 252 (c) 259 (d) 260
  18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 702 (c) 676 (d) 51
  19. 19.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 95 (b) 25 (c) 85 (d) 170
  20. 20.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 59 (d) 900
  21. 21.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 22 (c) 126 (d) 135
  22. 22.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 182 (c) 78 (d) 91
  23. 23.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 14 (b) 15 (c) 13 (d) 23
  24. 24.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 77 (b) 70 (c) 140 (d) 16
  25. 25.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 2628 (c) 2556 (d) 5256
  26. 26.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 70 (b) 35 (c) 13 (d) 38
  27. 27.What is the 27th term of the AP 3, 12, 21, 30, …? (a) 237 (b) 234 (c) 246 (d) 243
  28. 28.What is the 33rd term of the AP 1, 8, 15, 22, …? (a) 231 (b) 224 (c) 232 (d) 225
  29. 29.What is the 35th term of the AP 15, 20, 25, 30, …? (a) 170 (b) 190 (c) 175 (d) 185
  30. 30.What is the 11th term of the AP 4, 7, 10, 13, …? (a) 37 (b) 33 (c) 30 (d) 34
  31. 31.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 56 (b) 28 (c) 29 (d) 7
  32. 32.Which term of the AP 14, 18, 22, 26, … is 110? (a) 24th (b) 26th (c) 27th (d) 25th
  33. 33.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 96 (c) 81 (d) 162
  34. 34.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 72 (c) 16 (d) 80
  35. 35.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 435 (c) 870 (d) 436
  36. 36.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 11 (b) 12 (c) 10 (d) 13
  37. 37.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 296 (b) 168 (c) 148 (d) 36
  38. 38.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  39. 39.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 70 (c) 17 (d) 130
  40. 40.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 35 (c) 342 (d) 171

Answer key

  1. 2701
  2. 71
  3. 114
  4. 29
  5. 77
  6. 19th
  7. 2278
  8. 2775
  9. 100
  10. 100
  11. 186
  12. 378
  13. 83
  14. 39
  15. 28th
  16. 145
  17. 260
  18. 676
  19. 85
  20. 900
  21. 126
  22. 91
  23. 14
  24. 70
  25. 2628
  26. 35
  27. 237
  28. 225
  29. 185
  30. 34
  31. 28
  32. 25th
  33. 81
  34. 72
  35. 435
  36. 11
  37. 148
  38. 196
  39. 65
  40. 324

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