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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 711 · 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 missing term in the AP 8, 10, ?, 14, 16? (a) 12 (b) 11 (c) 14 (d) 13
  2. 2.What is the 20th term of the AP 10, 18, 26, 34, …? (a) 162 (b) 152 (c) 170 (d) 160
  3. 3.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 870 (c) 406 (d) 436
  4. 4.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 170 (b) 95 (c) 85 (d) 25
  5. 5.Which term of the AP 2, 5, 8, 11, … is 41? (a) 15th (b) 16th (c) 14th (d) 13th
  6. 6.What is the 13th term of the AP 2, 11, 20, 29, …? (a) 110 (b) 117 (c) 119 (d) 108
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  8. 8.What is the missing term in the AP 1, 8, 15, ?, 29? (a) 22 (b) 29 (c) 23 (d) 21
  9. 9.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 528 (c) 1122 (d) 561
  10. 10.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 20 (b) 28 (c) 21 (d) 22
  11. 11.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 29 (b) 27 (c) 28 (d) 36
  12. 12.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 7 (b) 15 (c) 8 (d) 9
  13. 13.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 19 (d) 110
  14. 14.What is the 10th term of the AP 13, 22, 31, 40, …? (a) 90 (b) 81 (c) 94 (d) 103
  15. 15.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 36 (b) 144 (c) 252 (d) 126
  16. 16.Which term of the AP 13, 21, 29, 37, … is 181? (a) 21st (b) 23rd (c) 24th (d) 22nd
  17. 17.Which term of the AP 6, 8, 10, 12, … is 26? (a) 10th (b) 11th (c) 12th (d) 13th
  18. 18.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 144 (b) 30 (c) 256 (d) 128
  19. 19.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 267 (c) 264 (d) 528
  20. 20.What is the 39th term of the AP 6, 10, 14, 18, …? (a) 156 (b) 158 (c) 152 (d) 162
  21. 21.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1891 (c) 1830 (d) 1892
  22. 22.What is the 32nd term of the AP 9, 11, 13, 15, …? (a) 73 (b) 64 (c) 71 (d) 62
  23. 23.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 4692 (c) 2278 (d) 2346
  24. 24.What is the 34th term of the AP 2, 9, 16, 23, …? (a) 238 (b) 233 (c) 231 (d) 240
  25. 25.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  26. 26.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  27. 27.What is the 21st term of the AP 1, 10, 19, 28, …? (a) 190 (b) 181 (c) 180 (d) 189
  28. 28.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 71 (b) 492 (c) 912 (d) 456
  29. 29.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 16 (b) 72 (c) 132 (d) 66
  30. 30.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 70 (d) 35
  31. 31.What is the 29th term of the AP 14, 23, 32, 41, …? (a) 275 (b) 261 (c) 252 (d) 266
  32. 32.What is the 28th term of the AP 4, 7, 10, 13, …? (a) 84 (b) 88 (c) 81 (d) 85
  33. 33.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  34. 34.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 176 (b) 200 (c) 43 (d) 352
  35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 171 (d) 35
  36. 36.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 23 (b) 24 (c) 25 (d) 26
  37. 37.What is the 39th term of the AP 20, 29, 38, 47, …? (a) 371 (b) 351 (c) 362 (d) 342
  38. 38.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 516 (b) 258 (c) 38 (d) 276
  39. 39.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 20 (b) 15 (c) 17 (d) 16
  40. 40.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 49 (d) 650

Answer key

  1. 12
  2. 162
  3. 435
  4. 85
  5. 14th
  6. 110
  7. 64
  8. 22
  9. 561
  10. 21
  11. 28
  12. 8
  13. 100
  14. 94
  15. 126
  16. 22nd
  17. 11th
  18. 128
  19. 264
  20. 158
  21. 1891
  22. 71
  23. 2346
  24. 233
  25. 441
  26. 900
  27. 181
  28. 456
  29. 66
  30. 35
  31. 266
  32. 85
  33. 196
  34. 176
  35. 324
  36. 24
  37. 362
  38. 258
  39. 16
  40. 625

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