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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 336 · 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 68? (a) 2346 (b) 2278 (c) 4692 (d) 2312
  2. 2.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 30 (b) 32 (c) 39 (d) 31
  3. 3.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1653 (c) 1711 (d) 1682
  4. 4.What is the 28th term of the AP 13, 16, 19, 22, …? (a) 84 (b) 81 (c) 94 (d) 97
  5. 5.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 55 (b) 60 (c) 110 (d) 10
  6. 6.What is the 24th term of the AP 9, 13, 17, 21, …? (a) 105 (b) 92 (c) 101 (d) 96
  7. 7.What is the missing term in the AP 11, 20, ?, 38, 47? (a) 30 (b) 28 (c) 38 (d) 29
  8. 8.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 49 (b) 50 (c) 10 (d) 98
  9. 9.What is the 19th term of the AP 1, 10, 19, 28, …? (a) 172 (b) 163 (c) 171 (d) 162
  10. 10.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 72 (b) 64 (c) 15 (d) 128
  11. 11.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1035 (c) 1036 (d) 2070
  12. 12.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 6 (b) 21 (c) 40 (d) 20
  13. 13.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 132 (b) 133 (c) 17 (d) 264
  14. 14.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 162 (b) 81 (c) 21 (d) 90
  15. 15.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 11 (b) 13 (c) 12 (d) 10
  16. 16.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 1891 (c) 1830 (d) 3782
  17. 17.Which term of the AP 4, 10, 16, 22, … is 130? (a) 22nd (b) 23rd (c) 21st (d) 24th
  18. 18.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 196 (b) 101 (c) 23 (d) 98
  19. 19.What is the 31st term of the AP 17, 21, 25, 29, …? (a) 141 (b) 120 (c) 124 (d) 137
  20. 20.Which term of the AP 7, 14, 21, 28, … is 217? (a) 33rd (b) 30th (c) 32nd (d) 31st
  21. 21.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 138 (b) 34 (c) 133 (d) 266
  22. 22.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 91 (d) 182
  23. 23.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 162 (b) 90 (c) 81 (d) 17
  24. 24.What is the 24th term of the AP 12, 19, 26, 33, …? (a) 180 (b) 161 (c) 168 (d) 173
  25. 25.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 81 (d) 17
  26. 26.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 540 (b) 275 (c) 50 (d) 270
  27. 27.What is the 27th term of the AP 6, 13, 20, 27, …? (a) 195 (b) 182 (c) 189 (d) 188
  28. 28.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 24 (b) 21 (c) 22 (d) 20
  29. 29.What is the 22nd term of the AP 11, 20, 29, 38, …? (a) 209 (b) 198 (c) 200 (d) 189
  30. 30.What is the sum of all the whole numbers from 1 to 60? (a) 1830 (b) 1800 (c) 1770 (d) 3660
  31. 31.What is the 26th term of the AP 17, 21, 25, 29, …? (a) 117 (b) 100 (c) 104 (d) 121
  32. 32.What is the 31st term of the AP 1, 5, 9, 13, …? (a) 120 (b) 121 (c) 124 (d) 125
  33. 33.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 21 (b) 16 (c) 14 (d) 15
  34. 34.What is the 18th term of the AP 3, 8, 13, 18, …? (a) 90 (b) 88 (c) 85 (d) 93
  35. 35.What is the 28th term of the AP 14, 21, 28, 35, …? (a) 210 (b) 189 (c) 196 (d) 203
  36. 36.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 70 (b) 75 (c) 24 (d) 140
  37. 37.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 528 (c) 512 (d) 496
  38. 38.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 10 (b) 11 (c) 9 (d) 15
  39. 39.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4372 (c) 4278 (d) 4371
  40. 40.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 150 (c) 23 (d) 75

Answer key

  1. 2346
  2. 31
  3. 1711
  4. 94
  5. 55
  6. 101
  7. 29
  8. 49
  9. 163
  10. 64
  11. 1035
  12. 20
  13. 132
  14. 81
  15. 11
  16. 1891
  17. 22nd
  18. 98
  19. 137
  20. 31st
  21. 133
  22. 169
  23. 81
  24. 173
  25. 81
  26. 270
  27. 188
  28. 21
  29. 200
  30. 1830
  31. 117
  32. 121
  33. 15
  34. 88
  35. 203
  36. 70
  37. 528
  38. 10
  39. 4371
  40. 75

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