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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 829 · 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 34th term of the AP 1, 6, 11, 16, …? (a) 170 (b) 171 (c) 165 (d) 166
  2. 2.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 3655 (c) 7310 (d) 3656
  3. 3.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 363 (b) 396 (c) 726 (d) 63
  4. 4.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 1980 (c) 990 (d) 968
  5. 5.What is the 30th term of the AP 2, 11, 20, 29, …? (a) 272 (b) 261 (c) 270 (d) 263
  6. 6.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2702 (c) 2701 (d) 5402
  7. 7.What is the 38th term of the AP 2, 5, 8, 11, …? (a) 111 (b) 113 (c) 116 (d) 114
  8. 8.Which term of the AP 10, 14, 18, 22, … is 46? (a) 9th (b) 12th (c) 10th (d) 11th
  9. 9.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 43 (b) 196 (c) 350 (d) 175
  10. 10.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 682 (b) 374 (c) 341 (d) 61
  11. 11.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 216 (b) 38 (c) 198 (d) 396
  12. 12.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 25 (b) 95 (c) 85 (d) 170
  13. 13.What is the 23rd term of the AP 14, 20, 26, 32, …? (a) 132 (b) 146 (c) 138 (d) 152
  14. 14.What is the 10th term of the AP 14, 16, 18, 20, …? (a) 34 (b) 32 (c) 18 (d) 20
  15. 15.What is the 17th term of the AP 16, 22, 28, 34, …? (a) 102 (b) 112 (c) 96 (d) 118
  16. 16.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 14 (b) 19 (c) 16 (d) 15
  17. 17.What is the missing term in the AP 13, 21, ?, 37, 45? (a) 29 (b) 30 (c) 28 (d) 37
  18. 18.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 65 (b) 75 (c) 130 (d) 21
  19. 19.What is the 31st term of the AP 10, 16, 22, 28, …? (a) 196 (b) 190 (c) 180 (d) 186
  20. 20.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 27 (d) 105
  21. 21.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 235 (b) 46 (c) 470 (d) 260
  22. 22.Which term of the AP 9, 13, 17, 21, … is 109? (a) 25th (b) 27th (c) 26th (d) 28th
  23. 23.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 440 (b) 223 (c) 35 (d) 220
  24. 24.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 456 (b) 30 (c) 228 (d) 240
  25. 25.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 140 (b) 38 (c) 161 (d) 280
  26. 26.What is the 37th term of the AP 20, 27, 34, 41, …? (a) 252 (b) 272 (c) 279 (d) 259
  27. 27.What is the 19th term of the AP 9, 11, 13, 15, …? (a) 36 (b) 38 (c) 47 (d) 45
  28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 9 (d) 25
  29. 29.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 1008 (b) 75 (c) 504 (d) 540
  30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 506 (d) 484
  31. 31.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 1482 (c) 722 (d) 741
  32. 32.What is the sum of all the whole numbers from 1 to 45? (a) 2070 (b) 1036 (c) 990 (d) 1035
  33. 33.What is the 22nd term of the AP 1, 9, 17, 25, …? (a) 176 (b) 168 (c) 169 (d) 177
  34. 34.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 55 (b) 110 (c) 60 (d) 21
  35. 35.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 70 (b) 140 (c) 22 (d) 80
  36. 36.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 72 (c) 11 (d) 36
  37. 37.What is the 14th term of the AP 8, 10, 12, 14, …? (a) 34 (b) 26 (c) 28 (d) 36
  38. 38.What is the 34th term of the AP 4, 7, 10, 13, …? (a) 99 (b) 106 (c) 103 (d) 102
  39. 39.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 1250 (c) 1275 (d) 2550
  40. 40.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 21 (b) 6 (c) 42 (d) 24

Answer key

  1. 166
  2. 3655
  3. 363
  4. 990
  5. 263
  6. 2701
  7. 113
  8. 10th
  9. 175
  10. 341
  11. 198
  12. 85
  13. 146
  14. 32
  15. 112
  16. 15
  17. 29
  18. 65
  19. 190
  20. 196
  21. 235
  22. 26th
  23. 220
  24. 228
  25. 140
  26. 272
  27. 45
  28. 25
  29. 504
  30. 484
  31. 741
  32. 1035
  33. 169
  34. 55
  35. 70
  36. 36
  37. 34
  38. 103
  39. 1275
  40. 21

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