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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 957 · 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 20th term of the AP 4, 12, 20, 28, …? (a) 152 (b) 156 (c) 160 (d) 164
  2. 2.Which term of the AP 5, 7, 9, 11, … is 49? (a) 22nd (b) 23rd (c) 24th (d) 25th
  3. 3.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1250 (c) 1225 (d) 1275
  4. 4.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 13 (b) 20 (c) 12 (d) 14
  5. 5.What is the 27th term of the AP 17, 26, 35, 44, …? (a) 260 (b) 234 (c) 243 (d) 251
  6. 6.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 45 (b) 275 (c) 297 (d) 550
  7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  8. 8.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 184 (b) 44 (c) 208 (d) 368
  9. 9.What is the 28th term of the AP 17, 21, 25, 29, …? (a) 129 (b) 108 (c) 125 (d) 112
  10. 10.What is the 10th term of the AP 11, 19, 27, 35, …? (a) 83 (b) 72 (c) 91 (d) 80
  11. 11.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 136 (c) 154 (d) 153
  12. 12.What is the 38th term of the AP 6, 9, 12, 15, …? (a) 117 (b) 120 (c) 114 (d) 111
  13. 13.What is the 26th term of the AP 10, 12, 14, 16, …? (a) 50 (b) 52 (c) 60 (d) 62
  14. 14.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 270 (b) 23 (c) 144 (d) 135
  15. 15.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 13 (b) 14 (c) 16 (d) 12
  16. 16.Which term of the AP 6, 12, 18, 24, … is 222? (a) 39th (b) 38th (c) 36th (d) 37th
  17. 17.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 132 (c) 55 (d) 67
  18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 361 (d) 190
  19. 19.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 34 (b) 133 (c) 138 (d) 266
  20. 20.What is the 22nd term of the AP 17, 26, 35, 44, …? (a) 215 (b) 206 (c) 189 (d) 198
  21. 21.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 35 (b) 26 (c) 27 (d) 28
  22. 22.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 231 (c) 232 (d) 462
  23. 23.What is the 29th term of the AP 20, 26, 32, 38, …? (a) 168 (b) 188 (c) 194 (d) 174
  24. 24.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 992 (d) 496
  25. 25.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 576 (b) 56 (c) 315 (d) 288
  26. 26.What is the 22nd term of the AP 18, 20, 22, 24, …? (a) 60 (b) 42 (c) 62 (d) 44
  27. 27.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 576 (d) 300
  28. 28.What is the 21st term of the AP 5, 11, 17, 23, …? (a) 131 (b) 120 (c) 125 (d) 126
  29. 29.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 216 (b) 196 (c) 42 (d) 392
  30. 30.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 75 (c) 78 (d) 150
  31. 31.Which term of the AP 5, 12, 19, 26, … is 117? (a) 17th (b) 18th (c) 16th (d) 19th
  32. 32.What is the 28th term of the AP 5, 9, 13, 17, …? (a) 117 (b) 108 (c) 113 (d) 112
  33. 33.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 440 (b) 220 (c) 240 (d) 45
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 136 (d) 272
  35. 35.Which term of the AP 3, 11, 19, 27, … is 59? (a) 9th (b) 10th (c) 7th (d) 8th
  36. 36.What is the 25th term of the AP 6, 9, 12, 15, …? (a) 75 (b) 78 (c) 81 (d) 72
  37. 37.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 58 (b) 732 (c) 366 (d) 396
  38. 38.Which term of the AP 10, 13, 16, 19, … is 52? (a) 14th (b) 16th (c) 17th (d) 15th
  39. 39.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 45 (c) 11 (d) 46
  40. 40.Which term of the AP 8, 16, 24, 32, … is 112? (a) 13th (b) 16th (c) 15th (d) 14th

Answer key

  1. 156
  2. 23rd
  3. 1275
  4. 13
  5. 251
  6. 275
  7. 25
  8. 184
  9. 125
  10. 83
  11. 153
  12. 117
  13. 60
  14. 135
  15. 13
  16. 37th
  17. 66
  18. 361
  19. 133
  20. 206
  21. 27
  22. 231
  23. 188
  24. 496
  25. 288
  26. 60
  27. 576
  28. 125
  29. 196
  30. 75
  31. 17th
  32. 113
  33. 220
  34. 256
  35. 8th
  36. 78
  37. 366
  38. 15th
  39. 45
  40. 14th

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