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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 434 · 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 sum of the first 5 terms of the AP 5, 7, 9, …? (a) 50 (b) 45 (c) 13 (d) 90
  2. 2.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 363 (b) 396 (c) 63 (d) 726
  3. 3.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 43 (b) 212 (c) 207 (d) 414
  4. 4.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 436 (c) 870 (d) 435
  5. 5.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 300 (d) 47
  6. 6.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 408 (b) 216 (c) 204 (d) 28
  7. 7.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 558 (b) 55 (c) 306 (d) 279
  8. 8.What is the 11th term of the AP 4, 10, 16, 22, …? (a) 60 (b) 70 (c) 64 (d) 66
  9. 9.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 45 (b) 46 (c) 9 (d) 90
  10. 10.What is the 23rd term of the AP 5, 10, 15, 20, …? (a) 120 (b) 116 (c) 115 (d) 110
  11. 11.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 820 (c) 1640 (d) 800
  12. 12.Which term of the AP 12, 14, 16, 18, … is 72? (a) 30th (b) 36th (c) 32nd (d) 31st
  13. 13.What is the 10th term of the AP 16, 24, 32, 40, …? (a) 80 (b) 96 (c) 88 (d) 72
  14. 14.Which term of the AP 5, 13, 21, 29, … is 117? (a) 15th (b) 17th (c) 14th (d) 16th
  15. 15.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 88 (c) 18 (d) 176
  16. 16.What is the 33rd term of the AP 8, 12, 16, 20, …? (a) 128 (b) 136 (c) 132 (d) 140
  17. 17.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 28 (b) 200 (c) 190 (d) 380
  18. 18.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 29 (b) 31 (c) 36 (d) 30
  19. 19.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 90 (b) 102 (c) 180 (d) 25
  20. 20.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 272 (b) 24 (c) 136 (d) 144
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  22. 22.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 136 (d) 272
  23. 23.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 7310 (c) 3656 (d) 3655
  24. 24.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 49 (b) 261 (c) 522 (d) 266
  25. 25.What is the 39th term of the AP 4, 10, 16, 22, …? (a) 234 (b) 228 (c) 238 (d) 232
  26. 26.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 13 (d) 28
  27. 27.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 57 (c) 384 (d) 354
  28. 28.What is the 40th term of the AP 8, 10, 12, 14, …? (a) 86 (b) 80 (c) 78 (d) 88
  29. 29.What is the 26th term of the AP 17, 26, 35, 44, …? (a) 251 (b) 225 (c) 234 (d) 242
  30. 30.What is the 19th term of the AP 9, 14, 19, 24, …? (a) 99 (b) 95 (c) 104 (d) 90
  31. 31.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 36 (b) 198 (c) 180 (d) 360
  32. 32.Which term of the AP 9, 15, 21, 27, … is 105? (a) 19th (b) 18th (c) 16th (d) 17th
  33. 33.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 55 (d) 784
  34. 34.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 25 (c) 320 (d) 170
  35. 35.What is the 25th term of the AP 4, 12, 20, 28, …? (a) 200 (b) 204 (c) 192 (d) 196
  36. 36.Which term of the AP 10, 18, 26, 34, … is 290? (a) 36th (b) 38th (c) 35th (d) 37th
  37. 37.What is the 10th term of the AP 15, 20, 25, 30, …? (a) 60 (b) 65 (c) 45 (d) 50
  38. 38.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 13 (b) 162 (c) 82 (d) 81
  39. 39.Which term of the AP 20, 22, 24, 26, … is 56? (a) 20th (b) 18th (c) 19th (d) 28th
  40. 40.What is the 10th term of the AP 10, 12, 14, 16, …? (a) 20 (b) 30 (c) 18 (d) 28

Answer key

  1. 45
  2. 363
  3. 207
  4. 435
  5. 576
  6. 204
  7. 279
  8. 64
  9. 45
  10. 115
  11. 820
  12. 31st
  13. 88
  14. 15th
  15. 88
  16. 136
  17. 190
  18. 30
  19. 90
  20. 136
  21. 169
  22. 256
  23. 3655
  24. 261
  25. 232
  26. 49
  27. 354
  28. 86
  29. 242
  30. 99
  31. 180
  32. 17th
  33. 784
  34. 160
  35. 196
  36. 36th
  37. 60
  38. 81
  39. 19th
  40. 28

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