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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 319 · 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 32nd term of the AP 18, 21, 24, 27, …? (a) 96 (b) 114 (c) 111 (d) 93
  2. 2.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 350 (b) 55 (c) 325 (d) 650
  3. 3.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 18 (b) 156 (c) 300 (d) 150
  4. 4.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 61 (b) 682 (c) 374 (d) 341
  5. 5.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 260 (b) 235 (c) 470 (d) 46
  6. 6.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 15 (b) 220 (c) 111 (d) 110
  7. 7.What is the 20th term of the AP 16, 19, 22, 25, …? (a) 73 (b) 57 (c) 76 (d) 60
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 51 (d) 676
  9. 9.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 968 (c) 946 (d) 1980
  10. 10.What is the 21st term of the AP 3, 10, 17, 24, …? (a) 143 (b) 150 (c) 147 (d) 140
  11. 11.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 180 (b) 90 (c) 91 (d) 14
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 729 (d) 53
  13. 13.What is the 28th term of the AP 17, 26, 35, 44, …? (a) 243 (b) 260 (c) 252 (d) 269
  14. 14.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 112 (b) 98 (c) 26 (d) 196
  15. 15.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78
  16. 16.Which term of the AP 8, 11, 14, 17, … is 86? (a) 26th (b) 29th (c) 27th (d) 28th
  17. 17.What is the 21st term of the AP 13, 15, 17, 19, …? (a) 40 (b) 55 (c) 53 (d) 42
  18. 18.What is the 11th term of the AP 9, 13, 17, 21, …? (a) 53 (b) 40 (c) 49 (d) 44
  19. 19.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 33 (b) 161 (c) 147 (d) 294
  20. 20.What is the sum of all the whole numbers from 1 to 89? (a) 3916 (b) 4006 (c) 8010 (d) 4005
  21. 21.What is the 32nd term of the AP 7, 12, 17, 22, …? (a) 160 (b) 162 (c) 167 (d) 155
  22. 22.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 45 (b) 240 (c) 440 (d) 220
  23. 23.Which term of the AP 17, 22, 27, 32, … is 167? (a) 30th (b) 32nd (c) 31st (d) 33rd
  24. 24.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 36 (b) 198 (c) 360 (d) 180
  25. 25.What is the missing term in the AP 16, 25, ?, 43, 52? (a) 33 (b) 35 (c) 34 (d) 43
  26. 26.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  27. 27.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 18 (b) 60 (c) 120 (d) 63
  28. 28.What is the 32nd term of the AP 1, 9, 17, 25, …? (a) 248 (b) 257 (c) 249 (d) 256
  29. 29.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 63 (b) 126 (c) 72 (d) 18
  30. 30.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 528 (b) 264 (c) 267 (d) 39
  31. 31.What is the 18th term of the AP 1, 7, 13, 19, …? (a) 102 (b) 108 (c) 103 (d) 109
  32. 32.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 46 (b) 217 (c) 196 (d) 392
  33. 33.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 240 (b) 120 (c) 136 (d) 29
  34. 34.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 325 (c) 300 (d) 650
  35. 35.What is the 40th term of the AP 9, 11, 13, 15, …? (a) 89 (b) 80 (c) 78 (d) 87
  36. 36.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 192 (c) 108 (d) 26
  37. 37.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 165 (b) 330 (c) 20 (d) 166
  38. 38.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 66 (c) 36 (d) 33
  39. 39.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 3322 (c) 6642 (d) 3240
  40. 40.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 133 (b) 34 (c) 138 (d) 266

Answer key

  1. 111
  2. 325
  3. 150
  4. 341
  5. 235
  6. 110
  7. 73
  8. 676
  9. 990
  10. 143
  11. 90
  12. 729
  13. 260
  14. 98
  15. 144
  16. 27th
  17. 53
  18. 49
  19. 147
  20. 4005
  21. 162
  22. 220
  23. 31st
  24. 180
  25. 34
  26. 100
  27. 60
  28. 249
  29. 63
  30. 264
  31. 103
  32. 196
  33. 120
  34. 325
  35. 87
  36. 96
  37. 165
  38. 33
  39. 3321
  40. 133

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