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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 680 · 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 15th term of the AP 18, 26, 34, 42, …? (a) 112 (b) 138 (c) 130 (d) 120
  2. 2.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 15 (b) 110 (c) 220 (d) 111
  3. 3.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 20 (b) 12 (c) 13 (d) 14
  4. 4.Which term of the AP 15, 23, 31, 39, … is 199? (a) 24th (b) 23rd (c) 26th (d) 25th
  5. 5.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 228 (b) 30 (c) 240 (d) 456
  6. 6.Which term of the AP 11, 18, 25, 32, … is 193? (a) 26th (b) 28th (c) 29th (d) 27th
  7. 7.Which term of the AP 12, 21, 30, 39, … is 192? (a) 21st (b) 22nd (c) 23rd (d) 20th
  8. 8.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 231 (d) 462
  9. 9.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 2016 (d) 1953
  10. 10.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 492 (b) 264 (c) 37 (d) 246
  11. 11.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 131 (b) 33 (c) 252 (d) 126
  12. 12.What is the 32nd term of the AP 20, 23, 26, 29, …? (a) 116 (b) 96 (c) 93 (d) 113
  13. 13.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 10 (b) 9 (c) 19 (d) 11
  14. 14.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 18 (b) 17 (c) 19 (d) 25
  15. 15.What is the 21st term of the AP 8, 16, 24, 32, …? (a) 160 (b) 176 (c) 169 (d) 168
  16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 43 (d) 506
  17. 17.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 72 (b) 144 (c) 80 (d) 16
  18. 18.What is the 36th term of the AP 2, 4, 6, 8, …? (a) 73 (b) 70 (c) 72 (d) 74
  19. 19.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 561 (c) 1190 (d) 578
  20. 20.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 406 (c) 435 (d) 436
  21. 21.What is the 35th term of the AP 4, 11, 18, 25, …? (a) 245 (b) 238 (c) 242 (d) 249
  22. 22.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 968 (c) 1980 (d) 990
  23. 23.What is the 34th term of the AP 9, 13, 17, 21, …? (a) 145 (b) 132 (c) 141 (d) 136
  24. 24.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 33 (b) 25 (c) 26 (d) 27
  25. 25.What is the 19th term of the AP 5, 14, 23, 32, …? (a) 171 (b) 162 (c) 167 (d) 176
  26. 26.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 440 (b) 880 (c) 473 (d) 70
  27. 27.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 351 (c) 702 (d) 325
  28. 28.What is the 10th term of the AP 19, 23, 27, 31, …? (a) 40 (b) 59 (c) 55 (d) 36
  29. 29.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 28 (b) 36 (c) 29 (d) 27
  30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  31. 31.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 180 (b) 30 (c) 90 (d) 105
  32. 32.What is the 33rd term of the AP 3, 5, 7, 9, …? (a) 69 (b) 66 (c) 64 (d) 67
  33. 33.Which term of the AP 16, 24, 32, 40, … is 328? (a) 39th (b) 42nd (c) 41st (d) 40th
  34. 34.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 204 (b) 120 (c) 32 (d) 102
  35. 35.What is the 16th term of the AP 20, 28, 36, 44, …? (a) 140 (b) 148 (c) 128 (d) 120
  36. 36.What is the 30th term of the AP 14, 17, 20, 23, …? (a) 90 (b) 101 (c) 104 (d) 87
  37. 37.Which term of the AP 7, 13, 19, 25, … is 115? (a) 21st (b) 19th (c) 20th (d) 18th
  38. 38.What is the 13th term of the AP 12, 21, 30, 39, …? (a) 108 (b) 129 (c) 117 (d) 120
  39. 39.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 50 (b) 26 (c) 25 (d) 7
  40. 40.What is the sum of all the whole numbers from 1 to 82? (a) 3321 (b) 3403 (c) 6806 (d) 3362

Answer key

  1. 130
  2. 110
  3. 13
  4. 24th
  5. 228
  6. 27th
  7. 21st
  8. 441
  9. 2016
  10. 246
  11. 126
  12. 113
  13. 10
  14. 18
  15. 168
  16. 484
  17. 72
  18. 72
  19. 595
  20. 435
  21. 242
  22. 990
  23. 141
  24. 26
  25. 167
  26. 440
  27. 351
  28. 55
  29. 28
  30. 100
  31. 90
  32. 67
  33. 40th
  34. 102
  35. 140
  36. 101
  37. 19th
  38. 120
  39. 25
  40. 3403

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