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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 84 · 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 all the whole numbers from 1 to 33? (a) 1122 (b) 562 (c) 528 (d) 561
  2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  3. 3.What is the 37th term of the AP 14, 16, 18, 20, …? (a) 74 (b) 88 (c) 86 (d) 72
  4. 4.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 69 (b) 19 (c) 138 (d) 78
  5. 5.Which term of the AP 15, 20, 25, 30, … is 210? (a) 41st (b) 39th (c) 40th (d) 42nd
  6. 6.Which term of the AP 19, 28, 37, 46, … is 235? (a) 26th (b) 25th (c) 27th (d) 24th
  7. 7.What is the 30th term of the AP 3, 8, 13, 18, …? (a) 150 (b) 145 (c) 153 (d) 148
  8. 8.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 19 (b) 15 (c) 14 (d) 13
  9. 9.What is the 13th term of the AP 11, 14, 17, 20, …? (a) 47 (b) 50 (c) 36 (d) 39
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 51 (d) 351
  11. 11.Which term of the AP 3, 8, 13, 18, … is 158? (a) 32nd (b) 34th (c) 33rd (d) 31st
  12. 12.What is the missing term in the AP 8, 11, ?, 17, 20? (a) 14 (b) 15 (c) 17 (d) 13
  13. 13.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 128 (b) 22 (c) 120 (d) 240
  14. 14.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 200 (b) 400 (c) 224 (d) 46
  15. 15.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 41 (d) 441
  16. 16.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 578 (c) 1190 (d) 595
  17. 17.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 23 (b) 24 (c) 22 (d) 21
  18. 18.What is the 23rd term of the AP 11, 18, 25, 32, …? (a) 172 (b) 154 (c) 165 (d) 161
  19. 19.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 100 (b) 200 (c) 19 (d) 110
  20. 20.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 468 (b) 504 (c) 72 (d) 936
  21. 21.What is the 26th term of the AP 11, 18, 25, 32, …? (a) 193 (b) 182 (c) 175 (d) 186
  22. 22.Which term of the AP 11, 19, 27, 35, … is 163? (a) 22nd (b) 20th (c) 21st (d) 19th
  23. 23.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 13 (b) 140 (c) 71 (d) 70
  24. 24.What is the missing term in the AP 20, ?, 36, 44, 52? (a) 28 (b) 27 (c) 29 (d) 36
  25. 25.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 78 (b) 42 (c) 9 (d) 39
  26. 26.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 182 (b) 19 (c) 91 (d) 98
  27. 27.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 290 (b) 160 (c) 145 (d) 28
  28. 28.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 17 (b) 22 (c) 18 (d) 19
  29. 29.What is the 35th term of the AP 11, 14, 17, 20, …? (a) 116 (b) 102 (c) 113 (d) 105
  30. 30.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 200 (b) 16 (c) 104 (d) 100
  31. 31.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 96 (b) 162 (c) 26 (d) 81
  32. 32.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 18 (b) 17 (c) 16 (d) 24
  33. 33.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 22 (c) 135 (d) 126
  34. 34.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 64 (b) 468 (c) 876 (d) 438
  35. 35.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 407 (b) 64 (c) 748 (d) 374
  36. 36.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 29 (d) 225
  37. 37.What is the missing term in the AP 19, 28, ?, 46, 55? (a) 38 (b) 36 (c) 46 (d) 37
  38. 38.What is the 38th term of the AP 5, 10, 15, 20, …? (a) 195 (b) 190 (c) 185 (d) 191
  39. 39.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 19 (b) 27 (c) 21 (d) 20
  40. 40.What is the 19th term of the AP 19, 27, 35, 43, …? (a) 171 (b) 152 (c) 144 (d) 163

Answer key

  1. 561
  2. 49
  3. 86
  4. 69
  5. 40th
  6. 25th
  7. 148
  8. 14
  9. 47
  10. 676
  11. 32nd
  12. 14
  13. 120
  14. 200
  15. 441
  16. 595
  17. 22
  18. 165
  19. 100
  20. 468
  21. 186
  22. 20th
  23. 70
  24. 28
  25. 39
  26. 91
  27. 145
  28. 18
  29. 113
  30. 100
  31. 81
  32. 17
  33. 126
  34. 438
  35. 374
  36. 225
  37. 37
  38. 190
  39. 20
  40. 163

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