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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 148 · 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 7 terms of the AP 3, 8, 13, …? (a) 131 (b) 252 (c) 33 (d) 126
  2. 2.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 110 (c) 60 (d) 55
  3. 3.What is the 32nd term of the AP 20, 23, 26, 29, …? (a) 93 (b) 116 (c) 96 (d) 113
  4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 231 (d) 441
  5. 5.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 325 (b) 55 (c) 350 (d) 650
  6. 6.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 19 (b) 150 (c) 145 (d) 290
  7. 7.What is the 25th term of the AP 11, 17, 23, 29, …? (a) 150 (b) 161 (c) 144 (d) 155
  8. 8.What is the 19th term of the AP 13, 18, 23, 28, …? (a) 95 (b) 90 (c) 103 (d) 108
  9. 9.What is the 26th term of the AP 10, 16, 22, 28, …? (a) 166 (b) 150 (c) 160 (d) 156
  10. 10.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1485 (c) 2970 (d) 1431
  11. 11.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 1122 (c) 561 (d) 562
  12. 12.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 1260 (c) 630 (d) 631
  13. 13.Which term of the AP 15, 17, 19, 21, … is 49? (a) 19th (b) 18th (c) 17th (d) 20th
  14. 14.What is the 17th term of the AP 11, 18, 25, 32, …? (a) 119 (b) 112 (c) 123 (d) 130
  15. 15.What is the 17th term of the AP 11, 13, 15, 17, …? (a) 43 (b) 45 (c) 32 (d) 34
  16. 16.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 35 (d) 342
  17. 17.What is the 35th term of the AP 10, 14, 18, 22, …? (a) 136 (b) 140 (c) 150 (d) 146
  18. 18.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 154 (c) 306 (d) 153
  19. 19.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 84 (b) 91 (c) 168 (d) 18
  20. 20.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 512 (c) 496 (d) 528
  21. 21.What is the 29th term of the AP 17, 20, 23, 26, …? (a) 104 (b) 87 (c) 101 (d) 84
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
  23. 23.What is the 12th term of the AP 14, 23, 32, 41, …? (a) 108 (b) 122 (c) 113 (d) 99
  24. 24.What is the 16th term of the AP 20, 28, 36, 44, …? (a) 148 (b) 128 (c) 120 (d) 140
  25. 25.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 104 (c) 10 (d) 52
  26. 26.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 9 (b) 11 (c) 10 (d) 19
  27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 21 (d) 36
  28. 28.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 24 (b) 70 (c) 75 (d) 140
  29. 29.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 15 (b) 9 (c) 10 (d) 11
  30. 30.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 180 (b) 90 (c) 95 (d) 28
  31. 31.What is the 16th term of the AP 10, 13, 16, 19, …? (a) 45 (b) 58 (c) 55 (d) 48
  32. 32.What is the 26th term of the AP 15, 24, 33, 42, …? (a) 249 (b) 234 (c) 225 (d) 240
  33. 33.What is the 16th term of the AP 16, 24, 32, 40, …? (a) 120 (b) 144 (c) 136 (d) 128
  34. 34.What is the 30th term of the AP 10, 18, 26, 34, …? (a) 240 (b) 242 (c) 232 (d) 250
  35. 35.What is the 40th term of the AP 4, 7, 10, 13, …? (a) 120 (b) 117 (c) 124 (d) 121
  36. 36.What is the sum of all the whole numbers from 1 to 73? (a) 5402 (b) 2701 (c) 2628 (d) 2702
  37. 37.Which term of the AP 5, 12, 19, 26, … is 82? (a) 11th (b) 12th (c) 14th (d) 13th
  38. 38.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 220 (b) 205 (c) 410 (d) 34
  39. 39.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 17 (b) 10 (c) 9 (d) 8
  40. 40.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 3080 (c) 1541 (d) 1485

Answer key

  1. 126
  2. 55
  3. 113
  4. 441
  5. 325
  6. 145
  7. 155
  8. 103
  9. 160
  10. 1485
  11. 561
  12. 630
  13. 18th
  14. 123
  15. 43
  16. 324
  17. 146
  18. 153
  19. 84
  20. 528
  21. 101
  22. 144
  23. 113
  24. 140
  25. 52
  26. 10
  27. 36
  28. 70
  29. 10
  30. 90
  31. 55
  32. 240
  33. 136
  34. 242
  35. 121
  36. 2701
  37. 12th
  38. 205
  39. 9
  40. 1540

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