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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 968 · 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 10, 13, 16, …? (a) 28 (b) 266 (c) 136 (d) 133
  2. 2.What is the 35th term of the AP 12, 16, 20, 24, …? (a) 136 (b) 140 (c) 152 (d) 148
  3. 3.What is the 33rd term of the AP 4, 8, 12, 16, …? (a) 133 (b) 132 (c) 128 (d) 136
  4. 4.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 190 (d) 380
  5. 5.What is the 29th term of the AP 17, 22, 27, 32, …? (a) 140 (b) 145 (c) 157 (d) 162
  6. 6.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 21 (b) 132 (c) 121 (d) 242
  7. 7.What is the 18th term of the AP 19, 25, 31, 37, …? (a) 108 (b) 102 (c) 121 (d) 127
  8. 8.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 21 (b) 20 (c) 28 (d) 19
  9. 9.What is the missing term in the AP 9, 14, ?, 24, 29? (a) 19 (b) 20 (c) 24 (d) 18
  10. 10.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4186 (c) 4278 (d) 4232
  11. 11.What is the 22nd term of the AP 4, 9, 14, 19, …? (a) 109 (b) 110 (c) 105 (d) 114
  12. 12.Which term of the AP 13, 22, 31, 40, … is 193? (a) 22nd (b) 20th (c) 21st (d) 23rd
  13. 13.What is the 38th term of the AP 9, 14, 19, 24, …? (a) 199 (b) 190 (c) 194 (d) 185
  14. 14.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 92 (c) 15 (d) 96
  15. 15.What is the 17th term of the AP 5, 7, 9, 11, …? (a) 34 (b) 32 (c) 39 (d) 37
  16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 42 (d) 11
  17. 17.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 15 (b) 11 (c) 10 (d) 12
  18. 18.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 140 (b) 270 (c) 135 (d) 18
  19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 43 (d) 484
  20. 20.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 162 (b) 30 (c) 165 (d) 324
  21. 21.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 8 (b) 12 (c) 9 (d) 10
  22. 22.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 120 (d) 225
  23. 23.Which term of the AP 19, 27, 35, 43, … is 187? (a) 23rd (b) 24th (c) 22nd (d) 21st
  24. 24.What is the 16th term of the AP 10, 18, 26, 34, …? (a) 120 (b) 128 (c) 130 (d) 138
  25. 25.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 34 (b) 132 (c) 228 (d) 114
  26. 26.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 102 (b) 204 (c) 27 (d) 114
  27. 27.Which term of the AP 5, 13, 21, 29, … is 125? (a) 17th (b) 16th (c) 15th (d) 18th
  28. 28.What is the 34th term of the AP 17, 20, 23, 26, …? (a) 102 (b) 99 (c) 119 (d) 116
  29. 29.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 19 (b) 11 (c) 10 (d) 12
  30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 110 (d) 55
  31. 31.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 168 (b) 336 (c) 180 (d) 25
  32. 32.What is the 36th term of the AP 1, 9, 17, 25, …? (a) 289 (b) 281 (c) 280 (d) 288
  33. 33.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 148 (b) 160 (c) 296 (d) 29
  34. 34.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 45 (c) 11 (d) 46
  35. 35.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 130 (b) 17 (c) 70 (d) 65
  36. 36.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 12 (b) 11 (c) 14 (d) 13
  37. 37.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 73 (b) 140 (c) 19 (d) 70
  38. 38.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 456 (b) 840 (c) 420 (d) 68
  39. 39.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 497 (c) 465 (d) 992
  40. 40.What is the 28th term of the AP 16, 18, 20, 22, …? (a) 70 (b) 72 (c) 56 (d) 54

Answer key

  1. 133
  2. 148
  3. 132
  4. 361
  5. 157
  6. 121
  7. 121
  8. 20
  9. 19
  10. 4278
  11. 109
  12. 21st
  13. 194
  14. 92
  15. 37
  16. 36
  17. 11
  18. 135
  19. 484
  20. 162
  21. 9
  22. 225
  23. 22nd
  24. 130
  25. 114
  26. 102
  27. 16th
  28. 116
  29. 11
  30. 100
  31. 168
  32. 281
  33. 148
  34. 45
  35. 65
  36. 12
  37. 70
  38. 420
  39. 496
  40. 70

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