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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 958 · 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 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 17 (c) 138 (d) 144
  2. 2.What is the 14th term of the AP 17, 19, 21, 23, …? (a) 26 (b) 45 (c) 28 (d) 43
  3. 3.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 1035 (c) 1081 (d) 2162
  4. 4.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 18 (b) 72 (c) 126 (d) 63
  5. 5.Which term of the AP 18, 24, 30, 36, … is 60? (a) 7th (b) 10th (c) 8th (d) 9th
  6. 6.What is the 27th term of the AP 16, 19, 22, 25, …? (a) 81 (b) 94 (c) 78 (d) 97
  7. 7.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3828 (c) 7832 (d) 3916
  8. 8.What is the 16th term of the AP 6, 8, 10, 12, …? (a) 36 (b) 32 (c) 30 (d) 38
  9. 9.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 176 (b) 89 (c) 13 (d) 88
  10. 10.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 1122 (c) 528 (d) 561
  11. 11.Which term of the AP 15, 19, 23, 27, … is 63? (a) 15th (b) 12th (c) 13th (d) 14th
  12. 12.Which term of the AP 15, 17, 19, 21, … is 91? (a) 39th (b) 38th (c) 41st (d) 40th
  13. 13.What is the 39th term of the AP 2, 5, 8, 11, …? (a) 117 (b) 119 (c) 116 (d) 114
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
  15. 15.What is the missing term in the AP 7, 14, ?, 28, 35? (a) 22 (b) 28 (c) 20 (d) 21
  16. 16.Which term of the AP 1, 7, 13, 19, … is 79? (a) 13th (b) 14th (c) 16th (d) 15th
  17. 17.What is the 23rd term of the AP 15, 22, 29, 36, …? (a) 161 (b) 176 (c) 154 (d) 169
  18. 18.What is the 12th term of the AP 7, 12, 17, 22, …? (a) 67 (b) 55 (c) 62 (d) 60
  19. 19.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 272 (c) 128 (d) 120
  20. 20.What is the sum of all the whole numbers from 1 to 39? (a) 1560 (b) 780 (c) 781 (d) 741
  21. 21.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 190 (b) 180 (c) 360 (d) 27
  22. 22.What is the 22nd term of the AP 4, 11, 18, 25, …? (a) 158 (b) 147 (c) 151 (d) 154
  23. 23.Which term of the AP 19, 22, 25, 28, … is 61? (a) 16th (b) 14th (c) 17th (d) 15th
  24. 24.What is the 19th term of the AP 18, 24, 30, 36, …? (a) 114 (b) 132 (c) 126 (d) 108
  25. 25.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2146 (c) 2080 (d) 2145
  26. 26.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 12 (b) 16 (c) 11 (d) 13
  27. 27.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 185 (b) 370 (c) 32 (d) 200
  28. 28.What is the 24th term of the AP 18, 21, 24, 27, …? (a) 90 (b) 72 (c) 69 (d) 87
  29. 29.What is the 31st term of the AP 17, 25, 33, 41, …? (a) 240 (b) 257 (c) 265 (d) 248
  30. 30.What is the 32nd term of the AP 15, 20, 25, 30, …? (a) 160 (b) 155 (c) 170 (d) 175
  31. 31.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 24 (b) 32 (c) 23 (d) 25
  32. 32.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 48 (b) 54 (c) 96 (d) 13
  33. 33.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 253 (c) 277 (d) 552
  34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 676 (d) 351
  35. 35.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 3660 (c) 1830 (d) 1800
  36. 36.What is the 14th term of the AP 5, 13, 21, 29, …? (a) 104 (b) 117 (c) 109 (d) 112
  37. 37.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 27 (b) 135 (c) 270 (d) 138
  38. 38.What is the missing term in the AP 13, ?, 19, 22, 25? (a) 15 (b) 19 (c) 17 (d) 16
  39. 39.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 260 (b) 470 (c) 46 (d) 235
  40. 40.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 336 (b) 168 (c) 42 (d) 189

Answer key

  1. 138
  2. 43
  3. 1081
  4. 63
  5. 8th
  6. 94
  7. 3916
  8. 36
  9. 88
  10. 561
  11. 13th
  12. 39th
  13. 116
  14. 64
  15. 21
  16. 14th
  17. 169
  18. 62
  19. 136
  20. 780
  21. 180
  22. 151
  23. 15th
  24. 126
  25. 2145
  26. 12
  27. 185
  28. 87
  29. 257
  30. 170
  31. 24
  32. 48
  33. 276
  34. 676
  35. 1830
  36. 109
  37. 135
  38. 16
  39. 235
  40. 168

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