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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 100 · 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 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 78 (d) 144
  2. 2.What is the 32nd term of the AP 20, 25, 30, 35, …? (a) 155 (b) 175 (c) 160 (d) 180
  3. 3.What is the 31st term of the AP 13, 16, 19, 22, …? (a) 103 (b) 90 (c) 93 (d) 106
  4. 4.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 18 (b) 17 (c) 16 (d) 15
  5. 5.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 55 (d) 50
  6. 6.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 160 (b) 144 (c) 32 (d) 288
  7. 7.Which term of the AP 17, 25, 33, 41, … is 297? (a) 37th (b) 38th (c) 35th (d) 36th
  8. 8.What is the 16th term of the AP 10, 19, 28, 37, …? (a) 144 (b) 154 (c) 135 (d) 145
  9. 9.What is the 38th term of the AP 9, 14, 19, 24, …? (a) 190 (b) 194 (c) 199 (d) 185
  10. 10.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 14 (b) 16 (c) 15 (d) 19
  11. 11.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 55 (d) 110
  12. 12.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 50 (b) 275 (c) 540 (d) 270
  13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  14. 14.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 780 (c) 1640 (d) 820
  15. 15.What is the 30th term of the AP 16, 20, 24, 28, …? (a) 120 (b) 136 (c) 132 (d) 116
  16. 16.What is the 17th term of the AP 12, 15, 18, 21, …? (a) 63 (b) 48 (c) 60 (d) 51
  17. 17.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 46 (b) 36 (c) 37 (d) 38
  18. 18.What is the 31st term of the AP 15, 17, 19, 21, …? (a) 62 (b) 77 (c) 60 (d) 75
  19. 19.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 98 (b) 23 (c) 101 (d) 196
  20. 20.What is the 17th term of the AP 15, 17, 19, 21, …? (a) 32 (b) 49 (c) 47 (d) 34
  21. 21.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 14 (b) 20 (c) 15 (d) 13
  22. 22.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 35 (b) 36 (c) 8 (d) 70
  23. 23.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 270 (b) 490 (c) 245 (d) 47
  24. 24.What is the 29th term of the AP 5, 13, 21, 29, …? (a) 229 (b) 237 (c) 232 (d) 224
  25. 25.Which term of the AP 8, 14, 20, 26, … is 62? (a) 12th (b) 9th (c) 11th (d) 10th
  26. 26.What is the 14th term of the AP 2, 6, 10, 14, …? (a) 58 (b) 56 (c) 52 (d) 54
  27. 27.What is the 16th term of the AP 13, 21, 29, 37, …? (a) 120 (b) 128 (c) 133 (d) 141
  28. 28.Which term of the AP 10, 16, 22, 28, … is 214? (a) 36th (b) 34th (c) 35th (d) 37th
  29. 29.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 638 (b) 341 (c) 319 (d) 49
  30. 30.Which term of the AP 13, 18, 23, 28, … is 143? (a) 27th (b) 26th (c) 29th (d) 28th
  31. 31.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
  32. 32.What is the missing term in the AP 7, 14, ?, 28, 35? (a) 22 (b) 28 (c) 21 (d) 20
  33. 33.What is the 30th term of the AP 18, 26, 34, 42, …? (a) 232 (b) 240 (c) 258 (d) 250
  34. 34.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 288 (b) 153 (c) 144 (d) 24
  35. 35.What is the 13th term of the AP 13, 19, 25, 31, …? (a) 78 (b) 72 (c) 85 (d) 91
  36. 36.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 156 (b) 30 (c) 312 (d) 168
  37. 37.What is the 18th term of the AP 15, 23, 31, 39, …? (a) 151 (b) 144 (c) 159 (d) 136
  38. 38.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 69 (b) 138 (c) 72 (d) 14
  39. 39.What is the 25th term of the AP 11, 16, 21, 26, …? (a) 136 (b) 125 (c) 120 (d) 131
  40. 40.What is the 19th term of the AP 15, 22, 29, 36, …? (a) 126 (b) 141 (c) 148 (d) 133

Answer key

  1. 144
  2. 175
  3. 103
  4. 16
  5. 55
  6. 144
  7. 36th
  8. 145
  9. 194
  10. 15
  11. 100
  12. 270
  13. 25
  14. 820
  15. 132
  16. 60
  17. 37
  18. 75
  19. 98
  20. 47
  21. 14
  22. 35
  23. 245
  24. 229
  25. 10th
  26. 54
  27. 133
  28. 35th
  29. 319
  30. 27th
  31. 225
  32. 21
  33. 250
  34. 144
  35. 85
  36. 156
  37. 151
  38. 69
  39. 131
  40. 141

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