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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 88 · 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 7 terms of the AP 5, 8, 11, …? (a) 101 (b) 196 (c) 23 (d) 98
  2. 2.What is the 21st term of the AP 13, 21, 29, 37, …? (a) 168 (b) 160 (c) 173 (d) 181
  3. 3.What is the 15th term of the AP 19, 24, 29, 34, …? (a) 94 (b) 89 (c) 70 (d) 75
  4. 4.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 4556 (c) 2278 (d) 2279
  5. 5.What is the 24th term of the AP 19, 21, 23, 25, …? (a) 46 (b) 67 (c) 48 (d) 65
  6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  7. 7.What is the 16th term of the AP 9, 16, 23, 30, …? (a) 121 (b) 105 (c) 114 (d) 112
  8. 8.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2016 (c) 4032 (d) 2017
  9. 9.What is the 35th term of the AP 7, 9, 11, 13, …? (a) 68 (b) 77 (c) 70 (d) 75
  10. 10.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 612 (c) 324 (d) 42
  11. 11.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 25 (b) 20 (c) 22 (d) 21
  12. 12.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1830 (c) 1800 (d) 1770
  13. 13.What is the 32nd term of the AP 15, 24, 33, 42, …? (a) 303 (b) 279 (c) 294 (d) 288
  14. 14.What is the 30th term of the AP 4, 9, 14, 19, …? (a) 149 (b) 150 (c) 145 (d) 154
  15. 15.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 264 (c) 504 (d) 252
  16. 16.Which term of the AP 10, 13, 16, 19, … is 79? (a) 25th (b) 26th (c) 23rd (d) 24th
  17. 17.What is the 12th term of the AP 10, 15, 20, 25, …? (a) 55 (b) 60 (c) 65 (d) 70
  18. 18.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 290 (b) 580 (c) 56 (d) 320
  19. 19.What is the 17th term of the AP 9, 18, 27, 36, …? (a) 162 (b) 144 (c) 153 (d) 154
  20. 20.What is the 13th term of the AP 18, 22, 26, 30, …? (a) 70 (b) 66 (c) 52 (d) 48
  21. 21.What is the 37th term of the AP 7, 11, 15, 19, …? (a) 151 (b) 144 (c) 148 (d) 155
  22. 22.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 210 (b) 108 (c) 105 (d) 24
  23. 23.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 112 (b) 108 (c) 216 (d) 17
  24. 24.What is the missing term in the AP 4, 13, ?, 31, 40? (a) 31 (b) 21 (c) 23 (d) 22
  25. 25.What is the 23rd term of the AP 12, 18, 24, 30, …? (a) 144 (b) 150 (c) 138 (d) 132
  26. 26.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 15 (b) 17 (c) 16 (d) 22
  27. 27.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 19 (b) 18 (c) 22 (d) 17
  28. 28.What is the 11th term of the AP 4, 8, 12, 16, …? (a) 45 (b) 48 (c) 40 (d) 44
  29. 29.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 260 (b) 44 (c) 520 (d) 280
  30. 30.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 14 (b) 72 (c) 138 (d) 69
  31. 31.What is the 25th term of the AP 2, 5, 8, 11, …? (a) 77 (b) 72 (c) 74 (d) 75
  32. 32.Which term of the AP 5, 10, 15, 20, … is 150? (a) 30th (b) 32nd (c) 31st (d) 29th
  33. 33.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 504 (b) 936 (c) 468 (d) 72
  34. 34.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 154 (c) 153 (d) 306
  35. 35.What is the 11th term of the AP 13, 17, 21, 25, …? (a) 53 (b) 57 (c) 44 (d) 40
  36. 36.What is the sum of all the whole numbers from 1 to 72? (a) 2628 (b) 2556 (c) 2592 (d) 5256
  37. 37.What is the 34th term of the AP 12, 15, 18, 21, …? (a) 114 (b) 111 (c) 99 (d) 102
  38. 38.What is the 34th term of the AP 1, 3, 5, 7, …? (a) 68 (b) 67 (c) 69 (d) 66
  39. 39.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 252 (b) 129 (c) 27 (d) 126
  40. 40.Which term of the AP 15, 24, 33, 42, … is 285? (a) 33rd (b) 30th (c) 31st (d) 32nd

Answer key

  1. 98
  2. 173
  3. 89
  4. 2278
  5. 65
  6. 121
  7. 114
  8. 2016
  9. 75
  10. 306
  11. 21
  12. 1830
  13. 294
  14. 149
  15. 252
  16. 24th
  17. 65
  18. 290
  19. 153
  20. 66
  21. 151
  22. 105
  23. 108
  24. 22
  25. 144
  26. 16
  27. 18
  28. 44
  29. 260
  30. 69
  31. 74
  32. 30th
  33. 468
  34. 153
  35. 53
  36. 2628
  37. 111
  38. 67
  39. 126
  40. 31st

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