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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 626 · 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 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 351 (d) 676
  2. 2.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 105 (b) 119 (c) 27 (d) 210
  3. 3.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 126 (c) 63 (d) 13
  4. 4.Which term of the AP 13, 17, 21, 25, … is 93? (a) 21st (b) 20th (c) 22nd (d) 23rd
  5. 5.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 144 (d) 78
  6. 6.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 352 (b) 50 (c) 660 (d) 330
  7. 7.What is the 12th term of the AP 4, 8, 12, 16, …? (a) 49 (b) 52 (c) 48 (d) 44
  8. 8.What is the 17th term of the AP 7, 11, 15, 19, …? (a) 64 (b) 68 (c) 71 (d) 75
  9. 9.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 224 (b) 112 (c) 31 (d) 117
  10. 10.What is the 13th term of the AP 4, 12, 20, 28, …? (a) 96 (b) 108 (c) 100 (d) 104
  11. 11.What is the 36th term of the AP 2, 6, 10, 14, …? (a) 140 (b) 144 (c) 142 (d) 146
  12. 12.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 277 (c) 276 (d) 552
  13. 13.Which term of the AP 5, 11, 17, 23, … is 167? (a) 27th (b) 28th (c) 29th (d) 30th
  14. 14.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 312 (b) 576 (c) 288 (d) 46
  15. 15.What is the 21st term of the AP 3, 9, 15, 21, …? (a) 120 (b) 123 (c) 129 (d) 126
  16. 16.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 110 (c) 55 (d) 45
  17. 17.Which term of the AP 17, 24, 31, 38, … is 73? (a) 8th (b) 11th (c) 10th (d) 9th
  18. 18.Which term of the AP 15, 19, 23, 27, … is 163? (a) 37th (b) 38th (c) 39th (d) 40th
  19. 19.What is the 15th term of the AP 17, 19, 21, 23, …? (a) 45 (b) 30 (c) 47 (d) 28
  20. 20.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 253 (d) 43
  21. 21.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 240 (d) 225
  22. 22.Which term of the AP 6, 14, 22, 30, … is 278? (a) 36th (b) 34th (c) 35th (d) 37th
  23. 23.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 294 (b) 147 (c) 168 (d) 39
  24. 24.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 20 (b) 17 (c) 18 (d) 19
  25. 25.What is the sum of all the whole numbers from 1 to 50? (a) 1250 (b) 1225 (c) 2550 (d) 1275
  26. 26.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 23 (b) 26 (c) 21 (d) 22
  27. 27.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4561 (c) 4465 (d) 9120
  28. 28.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 28 (b) 30 (c) 29 (d) 38
  29. 29.What is the 33rd term of the AP 1, 7, 13, 19, …? (a) 199 (b) 192 (c) 193 (d) 198
  30. 30.What is the 21st term of the AP 4, 8, 12, 16, …? (a) 85 (b) 88 (c) 84 (d) 80
  31. 31.What is the 13th term of the AP 5, 7, 9, 11, …? (a) 24 (b) 29 (c) 26 (d) 31
  32. 32.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 168 (b) 88 (c) 84 (d) 14
  33. 33.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 70 (b) 73 (c) 140 (d) 19
  34. 34.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 13 (b) 90 (c) 50 (d) 45
  35. 35.What is the 33rd term of the AP 3, 11, 19, 27, …? (a) 259 (b) 256 (c) 264 (d) 267
  36. 36.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 325 (c) 326 (d) 650
  37. 37.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 21 (b) 20 (c) 22 (d) 26
  38. 38.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210
  39. 39.What is the 21st term of the AP 20, 28, 36, 44, …? (a) 168 (b) 188 (c) 180 (d) 160
  40. 40.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 529 (d) 45

Answer key

  1. 676
  2. 105
  3. 63
  4. 21st
  5. 144
  6. 330
  7. 48
  8. 71
  9. 112
  10. 100
  11. 142
  12. 276
  13. 28th
  14. 288
  15. 123
  16. 55
  17. 9th
  18. 38th
  19. 45
  20. 484
  21. 225
  22. 35th
  23. 147
  24. 18
  25. 1275
  26. 22
  27. 4560
  28. 29
  29. 193
  30. 84
  31. 29
  32. 84
  33. 70
  34. 45
  35. 259
  36. 325
  37. 21
  38. 196
  39. 180
  40. 529

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