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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 805 · 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 70? (a) 2415 (b) 2450 (c) 2485 (d) 4970
  2. 2.What is the 16th term of the AP 18, 23, 28, 33, …? (a) 75 (b) 98 (c) 80 (d) 93
  3. 3.What is the 12th term of the AP 10, 19, 28, 37, …? (a) 118 (b) 109 (c) 99 (d) 108
  4. 4.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 231 (d) 210
  5. 5.What is the 20th term of the AP 6, 12, 18, 24, …? (a) 121 (b) 120 (c) 126 (d) 114
  6. 6.Which term of the AP 20, 24, 28, 32, … is 164? (a) 36th (b) 38th (c) 41st (d) 37th
  7. 7.Which term of the AP 4, 12, 20, 28, … is 244? (a) 32nd (b) 33rd (c) 31st (d) 30th
  8. 8.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2851 (c) 2850 (d) 2775
  9. 9.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 595 (c) 561 (d) 1190
  10. 10.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 56 (d) 49
  11. 11.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 55 (b) 650 (c) 350 (d) 325
  12. 12.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4851 (c) 4951 (d) 9900
  13. 13.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 252 (b) 264 (c) 32 (d) 504
  14. 14.What is the 23rd term of the AP 4, 13, 22, 31, …? (a) 198 (b) 202 (c) 207 (d) 211
  15. 15.Which term of the AP 8, 10, 12, 14, … is 26? (a) 11th (b) 13th (c) 9th (d) 10th
  16. 16.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 225 (c) 240 (d) 29
  17. 17.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 6 (b) 12 (c) 7 (d) 8
  18. 18.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 110 (b) 17 (c) 58 (d) 55
  19. 19.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 70 (b) 15 (c) 63 (d) 126
  20. 20.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 50 (b) 60 (c) 100 (d) 18
  21. 21.What is the 13th term of the AP 2, 7, 12, 17, …? (a) 60 (b) 67 (c) 65 (d) 62
  22. 22.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 41 (b) 182 (c) 322 (d) 161
  23. 23.What is the 29th term of the AP 14, 21, 28, 35, …? (a) 203 (b) 217 (c) 196 (d) 210
  24. 24.What is the 33rd term of the AP 6, 13, 20, 27, …? (a) 237 (b) 230 (c) 224 (d) 231
  25. 25.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 390 (b) 770 (c) 60 (d) 385
  26. 26.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 33 (d) 153
  27. 27.What is the 27th term of the AP 17, 22, 27, 32, …? (a) 152 (b) 130 (c) 147 (d) 135
  28. 28.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 45 (b) 12 (c) 40 (d) 80
  29. 29.Which term of the AP 6, 10, 14, 18, … is 82? (a) 19th (b) 22nd (c) 21st (d) 20th
  30. 30.What is the missing term in the AP 9, 11, ?, 15, 17? (a) 14 (b) 12 (c) 13 (d) 15
  31. 31.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 14 (b) 17 (c) 13 (d) 15
  32. 32.Which term of the AP 20, 24, 28, 32, … is 148? (a) 34th (b) 37th (c) 33rd (d) 32nd
  33. 33.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
  34. 34.What is the 11th term of the AP 14, 22, 30, 38, …? (a) 102 (b) 88 (c) 80 (d) 94
  35. 35.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 280 (b) 560 (c) 55 (d) 310
  36. 36.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 408 (b) 444 (c) 67 (d) 816
  37. 37.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 10 (b) 56 (c) 52 (d) 104
  38. 38.What is the 20th term of the AP 17, 24, 31, 38, …? (a) 157 (b) 133 (c) 140 (d) 150
  39. 39.Which term of the AP 6, 9, 12, 15, … is 57? (a) 20th (b) 19th (c) 17th (d) 18th
  40. 40.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 20 (b) 108 (c) 117 (d) 216

Answer key

  1. 2485
  2. 93
  3. 109
  4. 231
  5. 120
  6. 37th
  7. 31st
  8. 2850
  9. 595
  10. 49
  11. 325
  12. 4950
  13. 252
  14. 202
  15. 10th
  16. 225
  17. 7
  18. 55
  19. 63
  20. 50
  21. 62
  22. 161
  23. 210
  24. 230
  25. 385
  26. 289
  27. 147
  28. 40
  29. 20th
  30. 13
  31. 14
  32. 33rd
  33. 441
  34. 94
  35. 280
  36. 408
  37. 52
  38. 150
  39. 18th
  40. 108

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