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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 674 · 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 all the whole numbers from 1 to 64? (a) 2080 (b) 2016 (c) 2048 (d) 4160
  2. 2.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 100 (b) 30 (c) 105 (d) 200
  3. 3.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 484 (d) 506
  4. 4.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  5. 5.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 19 (b) 290 (c) 145 (d) 150
  6. 6.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 30 (b) 31 (c) 60 (d) 8
  7. 7.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 69 (b) 429 (c) 462 (d) 858
  8. 8.What is the 18th term of the AP 4, 11, 18, 25, …? (a) 123 (b) 126 (c) 130 (d) 119
  9. 9.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 272 (b) 52 (c) 248 (d) 496
  10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 17 (d) 90
  11. 11.What is the 35th term of the AP 16, 24, 32, 40, …? (a) 280 (b) 272 (c) 296 (d) 288
  12. 12.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 2557 (c) 5112 (d) 2556
  13. 13.What is the 13th term of the AP 17, 22, 27, 32, …? (a) 82 (b) 60 (c) 65 (d) 77
  14. 14.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 402 (b) 804 (c) 61 (d) 432
  15. 15.What is the 21st term of the AP 5, 11, 17, 23, …? (a) 120 (b) 131 (c) 125 (d) 126
  16. 16.What is the 32nd term of the AP 15, 20, 25, 30, …? (a) 160 (b) 175 (c) 155 (d) 170
  17. 17.Which term of the AP 8, 16, 24, 32, … is 128? (a) 16th (b) 15th (c) 18th (d) 17th
  18. 18.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 10 (b) 60 (c) 35 (d) 30
  19. 19.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 55 (d) 406
  20. 20.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 30 (b) 105 (c) 90 (d) 180
  21. 21.What is the 29th term of the AP 16, 25, 34, 43, …? (a) 277 (b) 268 (c) 261 (d) 252
  22. 22.What is the 28th term of the AP 10, 14, 18, 22, …? (a) 118 (b) 122 (c) 108 (d) 112
  23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  24. 24.Which term of the AP 4, 7, 10, 13, … is 64? (a) 20th (b) 22nd (c) 23rd (d) 21st
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 55 (d) 19
  26. 26.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 102 (b) 54 (c) 51 (d) 11
  27. 27.What is the missing term in the AP 18, 22, ?, 30, 34? (a) 30 (b) 26 (c) 25 (d) 27
  28. 28.What is the missing term in the AP 14, 21, 28, ?, 42? (a) 36 (b) 42 (c) 34 (d) 35
  29. 29.What is the 39th term of the AP 20, 24, 28, 32, …? (a) 156 (b) 152 (c) 176 (d) 172
  30. 30.What is the 36th term of the AP 11, 20, 29, 38, …? (a) 335 (b) 315 (c) 326 (d) 324
  31. 31.What is the 16th term of the AP 4, 6, 8, 10, …? (a) 34 (b) 32 (c) 36 (d) 30
  32. 32.What is the 32nd term of the AP 19, 27, 35, 43, …? (a) 275 (b) 256 (c) 267 (d) 248
  33. 33.What is the missing term in the AP 17, 25, 33, ?, 49? (a) 49 (b) 42 (c) 40 (d) 41
  34. 34.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 90 (b) 19 (c) 168 (d) 84
  35. 35.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 3160 (c) 3240 (d) 6480
  36. 36.What is the 12th term of the AP 8, 11, 14, 17, …? (a) 41 (b) 44 (c) 36 (d) 33
  37. 37.What is the 31st term of the AP 4, 11, 18, 25, …? (a) 221 (b) 214 (c) 217 (d) 210
  38. 38.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 660 (b) 50 (c) 330 (d) 352
  39. 39.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 780 (c) 820 (d) 1640
  40. 40.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 8 (b) 6 (c) 7 (d) 13

Answer key

  1. 2080
  2. 100
  3. 484
  4. 144
  5. 145
  6. 30
  7. 429
  8. 123
  9. 248
  10. 81
  11. 288
  12. 2556
  13. 77
  14. 402
  15. 125
  16. 170
  17. 16th
  18. 30
  19. 784
  20. 90
  21. 268
  22. 118
  23. 121
  24. 21st
  25. 100
  26. 51
  27. 26
  28. 35
  29. 172
  30. 326
  31. 34
  32. 267
  33. 41
  34. 84
  35. 3240
  36. 41
  37. 214
  38. 330
  39. 820
  40. 7

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