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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 131 · 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 16th term of the AP 15, 18, 21, 24, …? (a) 60 (b) 48 (c) 45 (d) 63
  2. 2.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4561 (c) 9120 (d) 4465
  3. 3.What is the 33rd term of the AP 20, 26, 32, 38, …? (a) 218 (b) 212 (c) 192 (d) 198
  4. 4.What is the missing term in the AP 16, 25, ?, 43, 52? (a) 35 (b) 33 (c) 43 (d) 34
  5. 5.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 100 (b) 115 (c) 200 (d) 32
  6. 6.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 6 (b) 24 (c) 42 (d) 21
  7. 7.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4656 (c) 4753 (d) 9506
  8. 8.What is the missing term in the AP 9, 16, ?, 30, 37? (a) 23 (b) 30 (c) 22 (d) 24
  9. 9.What is the 32nd term of the AP 19, 23, 27, 31, …? (a) 124 (b) 143 (c) 128 (d) 147
  10. 10.Which term of the AP 13, 19, 25, 31, … is 121? (a) 19th (b) 18th (c) 20th (d) 21st
  11. 11.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 153 (c) 154 (d) 306
  12. 12.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 12 (b) 13 (c) 11 (d) 19
  13. 13.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 49 (c) 650 (d) 325
  14. 14.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 288 (b) 144 (c) 162 (d) 39
  15. 15.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3487 (c) 3486 (d) 3403
  16. 16.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 14 (b) 9 (c) 10 (d) 11
  17. 17.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 16 (b) 5 (c) 30 (d) 15
  18. 18.What is the 10th term of the AP 8, 13, 18, 23, …? (a) 58 (b) 45 (c) 50 (d) 53
  19. 19.What is the 25th term of the AP 1, 10, 19, 28, …? (a) 216 (b) 225 (c) 217 (d) 226
  20. 20.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  21. 21.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 55 (c) 67 (d) 66
  22. 22.What is the 28th term of the AP 16, 25, 34, 43, …? (a) 243 (b) 252 (c) 268 (d) 259
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  24. 24.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 3160 (c) 3081 (d) 6320
  25. 25.What is the 33rd term of the AP 13, 15, 17, 19, …? (a) 79 (b) 66 (c) 64 (d) 77
  26. 26.What is the 36th term of the AP 3, 10, 17, 24, …? (a) 245 (b) 255 (c) 248 (d) 252
  27. 27.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 73 (b) 480 (c) 960 (d) 516
  28. 28.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 465 (d) 497
  29. 29.What is the 28th term of the AP 19, 24, 29, 34, …? (a) 159 (b) 135 (c) 140 (d) 154
  30. 30.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 120 (b) 114 (c) 15 (d) 228
  31. 31.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  32. 32.What is the missing term in the AP 12, 20, 28, ?, 44? (a) 44 (b) 36 (c) 37 (d) 35
  33. 33.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 27 (b) 252 (c) 126 (d) 129
  34. 34.What is the 39th term of the AP 16, 23, 30, 37, …? (a) 289 (b) 273 (c) 282 (d) 266
  35. 35.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 29 (b) 28 (c) 56 (d) 7
  36. 36.Which term of the AP 19, 22, 25, 28, … is 46? (a) 12th (b) 10th (c) 9th (d) 11th
  37. 37.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 27 (b) 20 (c) 18 (d) 19
  38. 38.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 26 (b) 27 (c) 35 (d) 25
  39. 39.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3081 (d) 3042
  40. 40.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 861 (c) 903 (d) 1806

Answer key

  1. 60
  2. 4560
  3. 212
  4. 34
  5. 100
  6. 21
  7. 4753
  8. 23
  9. 143
  10. 19th
  11. 153
  12. 12
  13. 625
  14. 144
  15. 3486
  16. 10
  17. 15
  18. 53
  19. 217
  20. 400
  21. 66
  22. 259
  23. 100
  24. 3160
  25. 77
  26. 248
  27. 480
  28. 496
  29. 154
  30. 114
  31. 441
  32. 36
  33. 126
  34. 282
  35. 28
  36. 10th
  37. 19
  38. 26
  39. 3081
  40. 903

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