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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 785 · 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 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 351 (d) 702
  2. 2.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 8 (b) 5 (c) 7 (d) 6
  3. 3.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 66 (b) 57 (c) 114 (d) 17
  4. 4.What is the 10th term of the AP 4, 12, 20, 28, …? (a) 76 (b) 80 (c) 84 (d) 72
  5. 5.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 756 (d) 53
  6. 6.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 900 (d) 59
  7. 7.What is the 37th term of the AP 1, 8, 15, 22, …? (a) 252 (b) 253 (c) 259 (d) 260
  8. 8.Which term of the AP 8, 16, 24, 32, … is 256? (a) 31st (b) 33rd (c) 32nd (d) 34th
  9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 57 (d) 841
  10. 10.What is the 27th term of the AP 15, 19, 23, 27, …? (a) 104 (b) 119 (c) 123 (d) 108
  11. 11.What is the 31st term of the AP 2, 11, 20, 29, …? (a) 279 (b) 272 (c) 281 (d) 270
  12. 12.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 4160 (c) 2080 (d) 2016
  13. 13.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 72 (d) 15
  14. 14.What is the 18th term of the AP 16, 18, 20, 22, …? (a) 50 (b) 52 (c) 34 (d) 36
  15. 15.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 576 (d) 300
  16. 16.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 210 (d) 400
  17. 17.What is the 34th term of the AP 20, 23, 26, 29, …? (a) 99 (b) 102 (c) 119 (d) 122
  18. 18.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 198 (b) 209 (c) 28 (d) 396
  19. 19.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 55 (b) 280 (c) 560 (d) 310
  20. 20.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 114 (b) 198 (c) 29 (d) 99
  21. 21.What is the 31st term of the AP 16, 21, 26, 31, …? (a) 171 (b) 150 (c) 166 (d) 155
  22. 22.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 16 (c) 5 (d) 15
  23. 23.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 3 (c) 4 (d) 5
  24. 24.What is the 32nd term of the AP 4, 10, 16, 22, …? (a) 196 (b) 192 (c) 190 (d) 186
  25. 25.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 216 (b) 228 (c) 432 (d) 29
  26. 26.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 110 (b) 19 (c) 200 (d) 100
  27. 27.What is the 19th term of the AP 19, 28, 37, 46, …? (a) 162 (b) 171 (c) 190 (d) 181
  28. 28.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 9 (b) 11 (c) 10 (d) 8
  29. 29.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 272 (d) 136
  30. 30.What is the 25th term of the AP 11, 20, 29, 38, …? (a) 216 (b) 225 (c) 236 (d) 227
  31. 31.What is the 35th term of the AP 20, 26, 32, 38, …? (a) 230 (b) 210 (c) 204 (d) 224
  32. 32.What is the 14th term of the AP 13, 19, 25, 31, …? (a) 84 (b) 78 (c) 91 (d) 97
  33. 33.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 6 (b) 5 (c) 4 (d) 9
  34. 34.What is the 10th term of the AP 9, 13, 17, 21, …? (a) 49 (b) 45 (c) 36 (d) 40
  35. 35.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 380 (d) 37
  36. 36.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 480 (c) 240 (d) 31
  37. 37.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4560 (c) 9312 (d) 4608
  38. 38.What is the 28th term of the AP 13, 22, 31, 40, …? (a) 243 (b) 265 (c) 252 (d) 256
  39. 39.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 325 (d) 49
  40. 40.What is the 39th term of the AP 5, 13, 21, 29, …? (a) 312 (b) 309 (c) 304 (d) 317

Answer key

  1. 676
  2. 6
  3. 57
  4. 76
  5. 729
  6. 900
  7. 253
  8. 32nd
  9. 841
  10. 119
  11. 272
  12. 2080
  13. 64
  14. 50
  15. 576
  16. 400
  17. 119
  18. 198
  19. 280
  20. 99
  21. 166
  22. 15
  23. 4
  24. 190
  25. 216
  26. 100
  27. 181
  28. 9
  29. 256
  30. 227
  31. 224
  32. 91
  33. 5
  34. 45
  35. 361
  36. 240
  37. 4656
  38. 256
  39. 625
  40. 309

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