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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 572 · 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 24th term of the AP 2, 10, 18, 26, …? (a) 184 (b) 192 (c) 186 (d) 194
  2. 2.What is the 26th term of the AP 16, 20, 24, 28, …? (a) 104 (b) 116 (c) 100 (d) 120
  3. 3.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 110 (b) 13 (c) 55 (d) 56
  4. 4.What is the 34th term of the AP 5, 7, 9, 11, …? (a) 71 (b) 66 (c) 73 (d) 68
  5. 5.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 40 (b) 10 (c) 41 (d) 80
  6. 6.What is the missing term in the AP 12, 20, 28, ?, 44? (a) 44 (b) 37 (c) 36 (d) 35
  7. 7.What is the 38th term of the AP 14, 18, 22, 26, …? (a) 148 (b) 162 (c) 166 (d) 152
  8. 8.What is the 13th term of the AP 7, 16, 25, 34, …? (a) 108 (b) 117 (c) 115 (d) 124
  9. 9.Which term of the AP 4, 7, 10, 13, … is 121? (a) 40th (b) 41st (c) 39th (d) 42nd
  10. 10.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 16 (b) 182 (c) 92 (d) 91
  11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 45 (d) 17
  12. 12.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4278 (c) 4186 (d) 4232
  13. 13.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2145 (c) 2080 (d) 2146
  14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 42 (d) 21
  15. 15.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 75 (c) 150 (d) 78
  16. 16.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 528 (b) 984 (c) 492 (d) 74
  17. 17.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 32 (b) 31 (c) 41 (d) 33
  18. 18.Which term of the AP 2, 8, 14, 20, … is 50? (a) 10th (b) 8th (c) 9th (d) 11th
  19. 19.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 38 (b) 164 (c) 328 (d) 184
  20. 20.What is the 21st term of the AP 2, 6, 10, 14, …? (a) 80 (b) 86 (c) 82 (d) 84
  21. 21.What is the 29th term of the AP 10, 16, 22, 28, …? (a) 178 (b) 184 (c) 174 (d) 168
  22. 22.What is the missing term in the AP 15, 17, ?, 21, 23? (a) 19 (b) 18 (c) 21 (d) 20
  23. 23.What is the 12th term of the AP 15, 22, 29, 36, …? (a) 77 (b) 84 (c) 92 (d) 99
  24. 24.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 161 (b) 33 (c) 294 (d) 147
  25. 25.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 756 (d) 729
  26. 26.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 180 (b) 360 (c) 36 (d) 198
  27. 27.What is the 35th term of the AP 12, 20, 28, 36, …? (a) 284 (b) 272 (c) 280 (d) 292
  28. 28.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 19 (b) 162 (c) 168 (d) 324
  29. 29.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 5 (b) 4 (c) 7 (d) 6
  30. 30.Which term of the AP 7, 14, 21, 28, … is 112? (a) 18th (b) 16th (c) 15th (d) 17th
  31. 31.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4372 (c) 4371 (d) 8742
  32. 32.What is the 15th term of the AP 1, 8, 15, 22, …? (a) 106 (b) 105 (c) 99 (d) 98
  33. 33.Which term of the AP 4, 13, 22, 31, … is 256? (a) 31st (b) 28th (c) 29th (d) 30th
  34. 34.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 50 (c) 45 (d) 55
  35. 35.Which term of the AP 11, 18, 25, 32, … is 67? (a) 11th (b) 9th (c) 10th (d) 8th
  36. 36.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 47 (b) 270 (c) 245 (d) 490
  37. 37.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 231 (d) 210
  38. 38.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 21 (b) 14 (c) 15 (d) 16
  39. 39.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 22 (b) 26 (c) 21 (d) 20
  40. 40.Which term of the AP 16, 23, 30, 37, … is 100? (a) 14th (b) 12th (c) 13th (d) 15th

Answer key

  1. 186
  2. 116
  3. 55
  4. 71
  5. 40
  6. 36
  7. 162
  8. 115
  9. 40th
  10. 91
  11. 81
  12. 4278
  13. 2145
  14. 36
  15. 75
  16. 492
  17. 32
  18. 9th
  19. 164
  20. 82
  21. 178
  22. 19
  23. 92
  24. 147
  25. 729
  26. 180
  27. 284
  28. 162
  29. 5
  30. 16th
  31. 4371
  32. 99
  33. 29th
  34. 55
  35. 9th
  36. 245
  37. 231
  38. 15
  39. 21
  40. 13th

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