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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 971 · 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 5 terms of the AP 9, 13, 17, …? (a) 85 (b) 95 (c) 170 (d) 25
  2. 2.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 28 (b) 27 (c) 34 (d) 26
  3. 3.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 528 (c) 562 (d) 561
  4. 4.What is the missing term in the AP 2, 9, 16, ?, 30? (a) 22 (b) 30 (c) 23 (d) 24
  5. 5.Which term of the AP 5, 10, 15, 20, … is 40? (a) 9th (b) 8th (c) 10th (d) 7th
  6. 6.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 57 (c) 870 (d) 435
  7. 7.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 27 (b) 170 (c) 90 (d) 85
  8. 8.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 28 (b) 27 (c) 35 (d) 26
  9. 9.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 270 (b) 486 (c) 51 (d) 243
  10. 10.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 34 (b) 180 (c) 162 (d) 324
  11. 11.What is the 37th term of the AP 11, 14, 17, 20, …? (a) 122 (b) 108 (c) 111 (d) 119
  12. 12.What is the 23rd term of the AP 14, 19, 24, 29, …? (a) 124 (b) 115 (c) 129 (d) 110
  13. 13.What is the 14th term of the AP 6, 10, 14, 18, …? (a) 62 (b) 56 (c) 52 (d) 58
  14. 14.Which term of the AP 20, 22, 24, 26, … is 72? (a) 36th (b) 28th (c) 27th (d) 26th
  15. 15.Which term of the AP 6, 13, 20, 27, … is 111? (a) 16th (b) 17th (c) 18th (d) 15th
  16. 16.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 66 (c) 132 (d) 67
  17. 17.What is the 35th term of the AP 15, 19, 23, 27, …? (a) 140 (b) 136 (c) 155 (d) 151
  18. 18.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 29 (d) 225
  19. 19.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 616 (b) 313 (c) 308 (d) 53
  20. 20.What is the missing term in the AP 20, ?, 32, 38, 44? (a) 27 (b) 25 (c) 32 (d) 26
  21. 21.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3570 (c) 3655 (d) 3656
  22. 22.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 200 (b) 23 (c) 100 (d) 112
  23. 23.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 20 (b) 96 (c) 180 (d) 90
  24. 24.What is the 38th term of the AP 16, 18, 20, 22, …? (a) 76 (b) 74 (c) 92 (d) 90
  25. 25.What is the 18th term of the AP 12, 20, 28, 36, …? (a) 148 (b) 136 (c) 144 (d) 156
  26. 26.What is the 20th term of the AP 7, 11, 15, 19, …? (a) 87 (b) 76 (c) 83 (d) 80
  27. 27.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 13 (b) 76 (c) 152 (d) 80
  28. 28.What is the 37th term of the AP 19, 25, 31, 37, …? (a) 216 (b) 235 (c) 241 (d) 222
  29. 29.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 40 (b) 360 (c) 200 (d) 180
  30. 30.Which term of the AP 19, 28, 37, 46, … is 118? (a) 11th (b) 13th (c) 14th (d) 12th
  31. 31.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 13 (b) 17 (c) 15 (d) 14
  32. 32.What is the 13th term of the AP 12, 18, 24, 30, …? (a) 90 (b) 72 (c) 78 (d) 84
  33. 33.Which term of the AP 14, 16, 18, 20, … is 78? (a) 34th (b) 33rd (c) 39th (d) 32nd
  34. 34.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 64 (b) 63 (c) 126 (d) 11
  35. 35.Which term of the AP 20, 27, 34, 41, … is 167? (a) 22nd (b) 23rd (c) 24th (d) 21st
  36. 36.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 58 (b) 396 (c) 732 (d) 366
  37. 37.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 39 (b) 336 (c) 168 (d) 173
  38. 38.What is the 16th term of the AP 5, 10, 15, 20, …? (a) 81 (b) 80 (c) 75 (d) 85
  39. 39.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 189 (b) 378 (c) 37 (d) 207
  40. 40.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 338 (c) 702 (d) 325

Answer key

  1. 85
  2. 27
  3. 561
  4. 23
  5. 8th
  6. 841
  7. 85
  8. 27
  9. 243
  10. 162
  11. 119
  12. 124
  13. 58
  14. 27th
  15. 16th
  16. 66
  17. 151
  18. 225
  19. 308
  20. 26
  21. 3655
  22. 100
  23. 90
  24. 90
  25. 148
  26. 83
  27. 76
  28. 235
  29. 180
  30. 12th
  31. 14
  32. 84
  33. 33rd
  34. 63
  35. 22nd
  36. 366
  37. 168
  38. 80
  39. 189
  40. 351

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