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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 325 · 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 20? (a) 190 (b) 210 (c) 420 (d) 200
  2. 2.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 35 (b) 33 (c) 34 (d) 41
  3. 3.What is the 17th term of the AP 18, 27, 36, 45, …? (a) 162 (b) 171 (c) 144 (d) 153
  4. 4.What is the 27th term of the AP 7, 9, 11, 13, …? (a) 54 (b) 52 (c) 59 (d) 61
  5. 5.Which term of the AP 13, 16, 19, 22, … is 61? (a) 19th (b) 16th (c) 17th (d) 18th
  6. 6.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 43 (b) 84 (c) 42 (d) 9
  7. 7.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  8. 8.Which term of the AP 18, 22, 26, 30, … is 114? (a) 26th (b) 27th (c) 25th (d) 24th
  9. 9.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 45 (b) 220 (c) 240 (d) 440
  10. 10.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 1352 (c) 1326 (d) 2756
  11. 11.What is the 15th term of the AP 6, 11, 16, 21, …? (a) 70 (b) 75 (c) 81 (d) 76
  12. 12.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 306 (d) 154
  13. 13.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 780 (c) 781 (d) 1560
  14. 14.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 255 (b) 48 (c) 510 (d) 280
  15. 15.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 16 (b) 12 (c) 14 (d) 13
  16. 16.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 161 (b) 182 (c) 322 (d) 41
  17. 17.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1458 (c) 2970 (d) 1485
  18. 18.What is the 14th term of the AP 4, 11, 18, 25, …? (a) 95 (b) 102 (c) 91 (d) 98
  19. 19.What is the 35th term of the AP 15, 20, 25, 30, …? (a) 175 (b) 185 (c) 190 (d) 170
  20. 20.What is the 21st term of the AP 6, 15, 24, 33, …? (a) 180 (b) 195 (c) 186 (d) 189
  21. 21.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 26 (b) 192 (c) 360 (d) 180
  22. 22.What is the 31st term of the AP 13, 18, 23, 28, …? (a) 163 (b) 168 (c) 155 (d) 150
  23. 23.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 228 (b) 420 (c) 34 (d) 210
  24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 17 (d) 45
  25. 25.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 166 (b) 161 (c) 322 (d) 38
  26. 26.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 300 (c) 326 (d) 325
  27. 27.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 41 (d) 231
  28. 28.What is the 11th term of the AP 3, 11, 19, 27, …? (a) 91 (b) 80 (c) 83 (d) 88
  29. 29.Which term of the AP 12, 15, 18, 21, … is 36? (a) 9th (b) 8th (c) 12th (d) 10th
  30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 253 (d) 43
  31. 31.What is the 18th term of the AP 6, 12, 18, 24, …? (a) 102 (b) 108 (c) 114 (d) 109
  32. 32.What is the missing term in the AP 15, ?, 29, 36, 43? (a) 23 (b) 21 (c) 29 (d) 22
  33. 33.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 276 (d) 45
  34. 34.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 354 (b) 57 (c) 708 (d) 384
  35. 35.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3042 (c) 3003 (d) 6162
  36. 36.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 92 (b) 16 (c) 91 (d) 182
  37. 37.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 780 (c) 800 (d) 1640
  38. 38.Which term of the AP 18, 26, 34, 42, … is 314? (a) 39th (b) 40th (c) 37th (d) 38th
  39. 39.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 64 (b) 126 (c) 12 (d) 63
  40. 40.What is the 37th term of the AP 16, 18, 20, 22, …? (a) 72 (b) 88 (c) 90 (d) 74

Answer key

  1. 210
  2. 34
  3. 162
  4. 59
  5. 17th
  6. 42
  7. 361
  8. 25th
  9. 220
  10. 1378
  11. 76
  12. 153
  13. 780
  14. 255
  15. 13
  16. 161
  17. 1485
  18. 95
  19. 185
  20. 186
  21. 180
  22. 163
  23. 210
  24. 81
  25. 161
  26. 325
  27. 441
  28. 83
  29. 9th
  30. 484
  31. 108
  32. 22
  33. 529
  34. 354
  35. 3081
  36. 91
  37. 820
  38. 38th
  39. 63
  40. 88

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