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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 600 · 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 the first 6 terms of the AP 2, 7, 12, …? (a) 102 (b) 27 (c) 87 (d) 174
  2. 2.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 240 (c) 105 (d) 120
  3. 3.What is the 15th term of the AP 10, 13, 16, 19, …? (a) 52 (b) 45 (c) 42 (d) 55
  4. 4.What is the 25th term of the AP 6, 15, 24, 33, …? (a) 225 (b) 231 (c) 222 (d) 216
  5. 5.What is the 33rd term of the AP 14, 23, 32, 41, …? (a) 311 (b) 297 (c) 302 (d) 288
  6. 6.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 21 (b) 20 (c) 19 (d) 18
  7. 7.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 300 (c) 650 (d) 325
  8. 8.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 40 (b) 180 (c) 350 (d) 175
  9. 9.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 8 (b) 10 (c) 9 (d) 7
  10. 10.What is the sum of all the whole numbers from 1 to 89? (a) 3916 (b) 8010 (c) 4006 (d) 4005
  11. 11.What is the 36th term of the AP 2, 5, 8, 11, …? (a) 105 (b) 107 (c) 110 (d) 108
  12. 12.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 58 (b) 310 (c) 340 (d) 620
  13. 13.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 702 (d) 676
  14. 14.What is the missing term in the AP 17, 20, ?, 26, 29? (a) 24 (b) 22 (c) 23 (d) 26
  15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
  16. 16.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 78 (c) 75 (d) 150
  17. 17.What is the 22nd term of the AP 9, 14, 19, 24, …? (a) 110 (b) 119 (c) 105 (d) 114
  18. 18.What is the 12th term of the AP 11, 16, 21, 26, …? (a) 55 (b) 66 (c) 71 (d) 60
  19. 19.What is the missing term in the AP 19, 23, ?, 31, 35? (a) 28 (b) 31 (c) 27 (d) 26
  20. 20.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 1260 (c) 630 (d) 595
  21. 21.What is the 11th term of the AP 18, 25, 32, 39, …? (a) 95 (b) 70 (c) 77 (d) 88
  22. 22.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 120 (d) 29
  24. 24.What is the 40th term of the AP 10, 15, 20, 25, …? (a) 205 (b) 210 (c) 200 (d) 195
  25. 25.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  26. 26.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 666 (c) 1332 (d) 630
  27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15
  28. 28.Which term of the AP 8, 17, 26, 35, … is 224? (a) 24th (b) 25th (c) 27th (d) 26th
  29. 29.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 378 (c) 756 (d) 351
  30. 30.What is the 29th term of the AP 1, 9, 17, 25, …? (a) 224 (b) 233 (c) 232 (d) 225
  31. 31.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 24 (b) 308 (c) 165 (d) 154
  32. 32.What is the missing term in the AP 18, 25, ?, 39, 46? (a) 33 (b) 39 (c) 32 (d) 31
  33. 33.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 187 (b) 374 (c) 27 (d) 198
  34. 34.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 264 (c) 252 (d) 504
  35. 35.What is the 28th term of the AP 1, 5, 9, 13, …? (a) 108 (b) 113 (c) 109 (d) 112
  36. 36.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 19 (b) 18 (c) 20 (d) 25
  37. 37.What is the 30th term of the AP 12, 19, 26, 33, …? (a) 215 (b) 203 (c) 222 (d) 210
  38. 38.What is the 14th term of the AP 9, 13, 17, 21, …? (a) 56 (b) 65 (c) 52 (d) 61
  39. 39.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 6480 (c) 3160 (d) 3200
  40. 40.What is the 31st term of the AP 19, 25, 31, 37, …? (a) 205 (b) 186 (c) 199 (d) 180

Answer key

  1. 87
  2. 120
  3. 52
  4. 222
  5. 302
  6. 19
  7. 325
  8. 175
  9. 8
  10. 4005
  11. 107
  12. 310
  13. 676
  14. 23
  15. 324
  16. 75
  17. 114
  18. 66
  19. 27
  20. 630
  21. 88
  22. 441
  23. 225
  24. 205
  25. 144
  26. 666
  27. 64
  28. 25th
  29. 378
  30. 225
  31. 154
  32. 32
  33. 187
  34. 252
  35. 109
  36. 19
  37. 215
  38. 61
  39. 3240
  40. 199

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