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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 181 · 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.Which term of the AP 3, 12, 21, 30, … is 84? (a) 12th (b) 11th (c) 9th (d) 10th
  2. 2.Which term of the AP 17, 23, 29, 35, … is 173? (a) 28th (b) 26th (c) 27th (d) 29th
  3. 3.What is the 26th term of the AP 19, 28, 37, 46, …? (a) 244 (b) 225 (c) 234 (d) 253
  4. 4.What is the 15th term of the AP 4, 11, 18, 25, …? (a) 109 (b) 105 (c) 98 (d) 102
  5. 5.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1568 (c) 1540 (d) 1596
  6. 6.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 12 (b) 75 (c) 80 (d) 150
  7. 7.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 3161 (c) 6320 (d) 3081
  8. 8.What is the 12th term of the AP 3, 7, 11, 15, …? (a) 48 (b) 51 (c) 47 (d) 44
  9. 9.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 74 (b) 984 (c) 528 (d) 492
  10. 10.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4560 (c) 4656 (d) 4608
  11. 11.Which term of the AP 15, 20, 25, 30, … is 210? (a) 39th (b) 41st (c) 40th (d) 42nd
  12. 12.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 210 (b) 33 (c) 120 (d) 105
  13. 13.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 108 (b) 16 (c) 216 (d) 109
  14. 14.Which term of the AP 5, 10, 15, 20, … is 105? (a) 20th (b) 22nd (c) 23rd (d) 21st
  15. 15.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 1596 (c) 1653 (d) 3306
  16. 16.What is the missing term in the AP 5, 14, ?, 32, 41? (a) 23 (b) 24 (c) 32 (d) 22
  17. 17.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 64 (b) 63 (c) 11 (d) 126
  18. 18.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 26 (b) 27 (c) 28 (d) 32
  19. 19.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 19 (b) 12 (c) 14 (d) 13
  20. 20.What is the 23rd term of the AP 4, 6, 8, 10, …? (a) 48 (b) 44 (c) 50 (d) 46
  21. 21.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 702 (d) 351
  22. 22.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  23. 23.What is the 12th term of the AP 7, 11, 15, 19, …? (a) 55 (b) 44 (c) 48 (d) 51
  24. 24.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729
  25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  26. 26.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1682 (c) 1711 (d) 1653
  27. 27.What is the 28th term of the AP 3, 9, 15, 21, …? (a) 162 (b) 165 (c) 171 (d) 168
  28. 28.Which term of the AP 14, 22, 30, 38, … is 70? (a) 7th (b) 8th (c) 9th (d) 10th
  29. 29.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 11 (b) 9 (c) 7 (d) 8
  30. 30.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 230 (b) 115 (c) 16 (d) 120
  31. 31.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 2485 (c) 5112 (d) 2556
  32. 32.What is the 10th term of the AP 8, 10, 12, 14, …? (a) 20 (b) 18 (c) 28 (d) 26
  33. 33.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 7 (b) 14 (c) 8 (d) 9
  34. 34.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 320 (c) 170 (d) 25
  35. 35.What is the 38th term of the AP 11, 13, 15, 17, …? (a) 85 (b) 76 (c) 74 (d) 87
  36. 36.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1129 (c) 1128 (d) 1081
  37. 37.What is the 39th term of the AP 3, 7, 11, 15, …? (a) 159 (b) 155 (c) 156 (d) 152
  38. 38.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 506 (c) 253 (d) 231
  39. 39.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 117 (b) 132 (c) 32 (d) 234
  40. 40.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 328 (b) 38 (c) 184 (d) 164

Answer key

  1. 10th
  2. 27th
  3. 244
  4. 102
  5. 1596
  6. 75
  7. 3160
  8. 47
  9. 492
  10. 4656
  11. 40th
  12. 105
  13. 108
  14. 21st
  15. 1653
  16. 23
  17. 63
  18. 27
  19. 13
  20. 48
  21. 351
  22. 100
  23. 51
  24. 729
  25. 25
  26. 1711
  27. 165
  28. 8th
  29. 8
  30. 115
  31. 2556
  32. 26
  33. 8
  34. 160
  35. 85
  36. 1128
  37. 155
  38. 253
  39. 117
  40. 164

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