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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 576 · 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 8 terms of the AP 2, 3, 4, …? (a) 48 (b) 44 (c) 88 (d) 9
  2. 2.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 6 (b) 9 (c) 4 (d) 5
  3. 3.What is the 40th term of the AP 14, 20, 26, 32, …? (a) 254 (b) 240 (c) 248 (d) 234
  4. 4.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 13 (b) 15 (c) 14 (d) 20
  5. 5.Which term of the AP 7, 16, 25, 34, … is 133? (a) 17th (b) 16th (c) 14th (d) 15th
  6. 6.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 4465 (c) 4371 (d) 8930
  7. 7.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 8 (b) 9 (c) 10 (d) 12
  8. 8.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 126 (b) 13 (c) 63 (d) 66
  9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 169 (d) 25
  10. 10.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 19 (b) 21 (c) 18 (d) 20
  11. 11.Which term of the AP 18, 20, 22, 24, … is 90? (a) 45th (b) 36th (c) 37th (d) 38th
  12. 12.What is the 14th term of the AP 3, 7, 11, 15, …? (a) 56 (b) 52 (c) 55 (d) 59
  13. 13.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 26 (b) 7 (c) 25 (d) 50
  14. 14.Which term of the AP 16, 23, 30, 37, … is 107? (a) 13th (b) 16th (c) 14th (d) 15th
  15. 15.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 140 (b) 85 (c) 26 (d) 70
  16. 16.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 319 (c) 297 (d) 47
  17. 17.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 81 (d) 17
  18. 18.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 42 (d) 21
  19. 19.Which term of the AP 20, 23, 26, 29, … is 92? (a) 25th (b) 26th (c) 24th (d) 27th
  20. 20.Which term of the AP 1, 4, 7, 10, … is 37? (a) 14th (b) 15th (c) 12th (d) 13th
  21. 21.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 70 (b) 73 (c) 140 (d) 19
  22. 22.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 192 (b) 384 (c) 45 (d) 216
  23. 23.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  24. 24.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  25. 25.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 55 (b) 310 (c) 280 (d) 560
  26. 26.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 110 (b) 21 (c) 60 (d) 55
  27. 27.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 242 (c) 506 (d) 253
  28. 28.What is the 22nd term of the AP 15, 20, 25, 30, …? (a) 125 (b) 120 (c) 110 (d) 105
  29. 29.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 3422 (c) 1711 (d) 1653
  30. 30.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 147 (b) 28 (c) 288 (d) 144
  31. 31.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 143 (b) 264 (c) 132 (d) 22
  32. 32.What is the 10th term of the AP 13, 21, 29, 37, …? (a) 80 (b) 85 (c) 93 (d) 72
  33. 33.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 1260 (c) 595 (d) 631
  34. 34.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 8 (b) 14 (c) 9 (d) 7
  35. 35.What is the 37th term of the AP 13, 22, 31, 40, …? (a) 333 (b) 324 (c) 337 (d) 346
  36. 36.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 34 (b) 26 (c) 24 (d) 25
  37. 37.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 136 (c) 31 (d) 272
  38. 38.What is the 25th term of the AP 18, 23, 28, 33, …? (a) 138 (b) 125 (c) 143 (d) 120
  39. 39.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 33 (b) 189 (c) 192 (d) 378
  40. 40.What is the 20th term of the AP 9, 12, 15, 18, …? (a) 57 (b) 69 (c) 60 (d) 66

Answer key

  1. 44
  2. 5
  3. 248
  4. 14
  5. 15th
  6. 4465
  7. 9
  8. 63
  9. 169
  10. 19
  11. 37th
  12. 55
  13. 25
  14. 14th
  15. 70
  16. 297
  17. 81
  18. 36
  19. 25th
  20. 13th
  21. 70
  22. 192
  23. 25
  24. 49
  25. 280
  26. 55
  27. 253
  28. 120
  29. 1711
  30. 144
  31. 132
  32. 85
  33. 630
  34. 8
  35. 337
  36. 25
  37. 256
  38. 138
  39. 189
  40. 66

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