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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 551 · 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 33rd term of the AP 7, 10, 13, 16, …? (a) 103 (b) 106 (c) 96 (d) 99
  2. 2.What is the sum of all the whole numbers from 1 to 92? (a) 4186 (b) 8556 (c) 4278 (d) 4232
  3. 3.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
  4. 4.Which term of the AP 8, 17, 26, 35, … is 197? (a) 23rd (b) 21st (c) 22nd (d) 24th
  5. 5.What is the 30th term of the AP 14, 21, 28, 35, …? (a) 203 (b) 224 (c) 217 (d) 210
  6. 6.What is the 31st term of the AP 12, 21, 30, 39, …? (a) 291 (b) 279 (c) 282 (d) 270
  7. 7.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  8. 8.Which term of the AP 3, 6, 9, 12, … is 27? (a) 11th (b) 10th (c) 9th (d) 8th
  9. 9.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 40 (b) 440 (c) 240 (d) 220
  10. 10.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 12 (c) 11 (d) 15
  11. 11.What is the 11th term of the AP 11, 16, 21, 26, …? (a) 55 (b) 66 (c) 50 (d) 61
  12. 12.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 154 (b) 280 (c) 140 (d) 32
  13. 13.What is the 17th term of the AP 17, 26, 35, 44, …? (a) 144 (b) 161 (c) 170 (d) 153
  14. 14.What is the 12th term of the AP 10, 15, 20, 25, …? (a) 70 (b) 60 (c) 65 (d) 55
  15. 15.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 162 (b) 81 (c) 13 (d) 82
  16. 16.What is the 34th term of the AP 10, 13, 16, 19, …? (a) 109 (b) 112 (c) 102 (d) 99
  17. 17.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 702 (d) 51
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  19. 19.Which term of the AP 12, 14, 16, 18, … is 42? (a) 21st (b) 15th (c) 16th (d) 17th
  20. 20.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 2485 (c) 2556 (d) 5112
  21. 21.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 240 (b) 480 (c) 51 (d) 264
  22. 22.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 198 (c) 203 (d) 42
  23. 23.Which term of the AP 11, 14, 17, 20, … is 44? (a) 12th (b) 11th (c) 13th (d) 14th
  24. 24.Which term of the AP 18, 21, 24, 27, … is 90? (a) 30th (b) 24th (c) 26th (d) 25th
  25. 25.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 150 (b) 156 (c) 300 (d) 18
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 435 (d) 870
  27. 27.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 1032 (b) 76 (c) 552 (d) 516
  28. 28.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 504 (c) 540 (d) 1008
  29. 29.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 7 (b) 29 (c) 56 (d) 28
  30. 30.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 105 (c) 98 (d) 210
  31. 31.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 32 (b) 25 (c) 24 (d) 23
  32. 32.Which term of the AP 12, 16, 20, 24, … is 116? (a) 29th (b) 28th (c) 27th (d) 26th
  33. 33.What is the 37th term of the AP 10, 15, 20, 25, …? (a) 195 (b) 185 (c) 190 (d) 180
  34. 34.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 10 (b) 108 (c) 54 (d) 55
  35. 35.What is the missing term in the AP 16, ?, 28, 34, 40? (a) 28 (b) 23 (c) 22 (d) 21
  36. 36.What is the 38th term of the AP 2, 7, 12, 17, …? (a) 185 (b) 190 (c) 187 (d) 192
  37. 37.What is the 19th term of the AP 16, 23, 30, 37, …? (a) 149 (b) 142 (c) 126 (d) 133
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 39 (c) 210 (d) 400
  39. 39.What is the 18th term of the AP 14, 16, 18, 20, …? (a) 48 (b) 50 (c) 36 (d) 34
  40. 40.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 37 (b) 156 (c) 176 (d) 312

Answer key

  1. 103
  2. 4278
  3. 25
  4. 22nd
  5. 217
  6. 282
  7. 784
  8. 9th
  9. 220
  10. 11
  11. 61
  12. 140
  13. 161
  14. 65
  15. 81
  16. 109
  17. 676
  18. 81
  19. 16th
  20. 2556
  21. 240
  22. 198
  23. 12th
  24. 25th
  25. 150
  26. 841
  27. 516
  28. 504
  29. 28
  30. 105
  31. 24
  32. 27th
  33. 190
  34. 54
  35. 22
  36. 187
  37. 142
  38. 400
  39. 48
  40. 156

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