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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 53 · 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 22nd term of the AP 10, 16, 22, 28, …? (a) 126 (b) 136 (c) 142 (d) 132
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 36 (d) 72
  3. 3.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 39 (b) 210 (c) 420 (d) 230
  4. 4.What is the 32nd term of the AP 15, 18, 21, 24, …? (a) 93 (b) 108 (c) 96 (d) 111
  5. 5.What is the 39th term of the AP 15, 17, 19, 21, …? (a) 76 (b) 78 (c) 91 (d) 93
  6. 6.What is the 26th term of the AP 3, 5, 7, 9, …? (a) 50 (b) 53 (c) 55 (d) 52
  7. 7.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 38 (b) 384 (c) 208 (d) 192
  8. 8.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 506 (c) 38 (d) 253
  9. 9.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 992 (c) 465 (d) 496
  10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  11. 11.What is the 34th term of the AP 13, 22, 31, 40, …? (a) 306 (b) 319 (c) 310 (d) 297
  12. 12.What is the 35th term of the AP 5, 14, 23, 32, …? (a) 320 (b) 306 (c) 315 (d) 311
  13. 13.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 35 (b) 336 (c) 168 (d) 184
  14. 14.What is the 33rd term of the AP 16, 21, 26, 31, …? (a) 165 (b) 160 (c) 176 (d) 181
  15. 15.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 462 (b) 36 (c) 234 (d) 231
  16. 16.What is the missing term in the AP 9, 14, ?, 24, 29? (a) 20 (b) 24 (c) 19 (d) 18
  17. 17.What is the 30th term of the AP 1, 5, 9, 13, …? (a) 121 (b) 116 (c) 120 (d) 117
  18. 18.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 13 (b) 12 (c) 14 (d) 16
  19. 19.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 1008 (b) 540 (c) 504 (d) 75
  20. 20.Which term of the AP 4, 8, 12, 16, … is 136? (a) 36th (b) 35th (c) 33rd (d) 34th
  21. 21.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 812 (c) 55 (d) 406
  22. 22.Which term of the AP 2, 9, 16, 23, … is 149? (a) 21st (b) 24th (c) 22nd (d) 23rd
  23. 23.What is the 26th term of the AP 5, 7, 9, 11, …? (a) 50 (b) 55 (c) 52 (d) 57
  24. 24.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 1225 (c) 1176 (d) 2450
  25. 25.What is the 29th term of the AP 1, 9, 17, 25, …? (a) 232 (b) 233 (c) 225 (d) 224
  26. 26.What is the 10th term of the AP 3, 5, 7, 9, …? (a) 18 (b) 20 (c) 21 (d) 23
  27. 27.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
  28. 28.Which term of the AP 5, 10, 15, 20, … is 80? (a) 16th (b) 15th (c) 18th (d) 17th
  29. 29.What is the 33rd term of the AP 10, 14, 18, 22, …? (a) 142 (b) 128 (c) 132 (d) 138
  30. 30.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 267 (b) 528 (c) 39 (d) 264
  31. 31.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 182 (b) 203 (c) 44 (d) 364
  32. 32.What is the 38th term of the AP 6, 14, 22, 30, …? (a) 310 (b) 296 (c) 304 (d) 302
  33. 33.What is the sum of all the whole numbers from 1 to 67? (a) 2279 (b) 2278 (c) 2211 (d) 4556
  34. 34.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 138 (b) 14 (c) 72 (d) 69
  35. 35.What is the 39th term of the AP 17, 20, 23, 26, …? (a) 114 (b) 131 (c) 134 (d) 117
  36. 36.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 242 (b) 121 (c) 16 (d) 122
  37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  38. 38.Which term of the AP 3, 6, 9, 12, … is 117? (a) 39th (b) 41st (c) 40th (d) 38th
  39. 39.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 169 (d) 25
  40. 40.What is the 15th term of the AP 16, 20, 24, 28, …? (a) 76 (b) 56 (c) 60 (d) 72

Answer key

  1. 136
  2. 64
  3. 210
  4. 108
  5. 91
  6. 53
  7. 192
  8. 253
  9. 496
  10. 81
  11. 310
  12. 311
  13. 168
  14. 176
  15. 231
  16. 19
  17. 117
  18. 13
  19. 504
  20. 34th
  21. 784
  22. 22nd
  23. 55
  24. 1225
  25. 225
  26. 21
  27. 400
  28. 16th
  29. 138
  30. 264
  31. 182
  32. 302
  33. 2278
  34. 69
  35. 131
  36. 121
  37. 144
  38. 39th
  39. 169
  40. 72

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