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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 55 · 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 26th term of the AP 3, 6, 9, 12, …? (a) 75 (b) 79 (c) 78 (d) 81
  2. 2.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 41 (b) 34 (c) 35 (d) 33
  3. 3.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 372 (b) 56 (c) 684 (d) 342
  4. 4.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 12 (b) 13 (c) 16 (d) 14
  5. 5.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 176 (b) 43 (c) 200 (d) 352
  6. 6.What is the missing term in the AP 19, 26, ?, 40, 47? (a) 40 (b) 34 (c) 32 (d) 33
  7. 7.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 48 (b) 312 (c) 336 (d) 624
  8. 8.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 95 (b) 25 (c) 85 (d) 170
  9. 9.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 162 (b) 81 (c) 90 (d) 17
  10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 153 (d) 33
  11. 11.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2485 (c) 4970 (d) 2415
  12. 12.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 660 (b) 352 (c) 50 (d) 330
  13. 13.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 23 (b) 25 (c) 28 (d) 24
  14. 14.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 21 (d) 42
  16. 16.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 429 (b) 69 (c) 858 (d) 462
  17. 17.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 176 (b) 187 (c) 26 (d) 352
  18. 18.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2146 (c) 2145 (d) 2080
  19. 19.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 27 (b) 24 (c) 23 (d) 22
  20. 20.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 30 (b) 180 (c) 105 (d) 90
  21. 21.What is the 33rd term of the AP 13, 18, 23, 28, …? (a) 160 (b) 165 (c) 173 (d) 178
  22. 22.What is the 36th term of the AP 3, 9, 15, 21, …? (a) 219 (b) 210 (c) 213 (d) 216
  23. 23.Which term of the AP 14, 16, 18, 20, … is 82? (a) 36th (b) 41st (c) 34th (d) 35th
  24. 24.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 121 (c) 240 (d) 120
  25. 25.What is the 28th term of the AP 16, 23, 30, 37, …? (a) 205 (b) 196 (c) 212 (d) 189
  26. 26.Which term of the AP 6, 8, 10, 12, … is 84? (a) 42nd (b) 40th (c) 39th (d) 41st
  27. 27.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 104 (b) 208 (c) 112 (d) 20
  28. 28.What is the 33rd term of the AP 1, 5, 9, 13, …? (a) 128 (b) 132 (c) 129 (d) 133
  29. 29.Which term of the AP 19, 28, 37, 46, … is 334? (a) 37th (b) 36th (c) 38th (d) 35th
  30. 30.What is the 23rd term of the AP 5, 12, 19, 26, …? (a) 166 (b) 159 (c) 154 (d) 161
  31. 31.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 16 (b) 11 (c) 12 (d) 13
  32. 32.What is the 21st term of the AP 1, 5, 9, 13, …? (a) 81 (b) 80 (c) 84 (d) 85
  33. 33.What is the 32nd term of the AP 13, 15, 17, 19, …? (a) 77 (b) 75 (c) 62 (d) 64
  34. 34.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 48 (b) 42 (c) 12 (d) 84
  35. 35.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 39 (b) 78 (c) 42 (d) 9
  36. 36.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 63 (b) 15 (c) 126 (d) 70
  37. 37.What is the 13th term of the AP 1, 10, 19, 28, …? (a) 117 (b) 108 (c) 118 (d) 109
  38. 38.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 138 (b) 69 (c) 78 (d) 19
  39. 39.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 16 (b) 15 (c) 17 (d) 25
  40. 40.Which term of the AP 2, 9, 16, 23, … is 93? (a) 16th (b) 15th (c) 14th (d) 13th

Answer key

  1. 78
  2. 34
  3. 342
  4. 13
  5. 176
  6. 33
  7. 312
  8. 85
  9. 81
  10. 289
  11. 2485
  12. 330
  13. 24
  14. 256
  15. 36
  16. 429
  17. 176
  18. 2145
  19. 23
  20. 90
  21. 173
  22. 213
  23. 35th
  24. 120
  25. 205
  26. 40th
  27. 104
  28. 129
  29. 36th
  30. 159
  31. 12
  32. 81
  33. 75
  34. 42
  35. 39
  36. 63
  37. 109
  38. 69
  39. 16
  40. 14th

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