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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 807 · 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 17th term of the AP 19, 23, 27, 31, …? (a) 87 (b) 68 (c) 83 (d) 64
  2. 2.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 946 (c) 1892 (d) 903
  3. 3.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 23 (b) 130 (c) 70 (d) 65
  4. 4.Which term of the AP 1, 10, 19, 28, … is 316? (a) 38th (b) 37th (c) 35th (d) 36th
  5. 5.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 12 (b) 11 (c) 16 (d) 13
  6. 6.What is the 32nd term of the AP 20, 29, 38, 47, …? (a) 288 (b) 308 (c) 279 (d) 299
  7. 7.Which term of the AP 1, 3, 5, 7, … is 59? (a) 32nd (b) 31st (c) 29th (d) 30th
  8. 8.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 105 (b) 182 (c) 91 (d) 25
  9. 9.What is the 14th term of the AP 5, 9, 13, 17, …? (a) 52 (b) 57 (c) 61 (d) 56
  10. 10.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 250 (b) 37 (c) 470 (d) 235
  11. 11.What is the 23rd term of the AP 8, 14, 20, 26, …? (a) 138 (b) 146 (c) 132 (d) 140
  12. 12.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 114 (b) 34 (c) 132 (d) 228
  13. 13.Which term of the AP 3, 5, 7, 9, … is 57? (a) 27th (b) 29th (c) 28th (d) 30th
  14. 14.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 220 (b) 30 (c) 440 (d) 231
  15. 15.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 930 (c) 900 (d) 465
  16. 16.What is the 39th term of the AP 11, 18, 25, 32, …? (a) 277 (b) 273 (c) 266 (d) 284
  17. 17.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 18 (b) 21 (c) 20 (d) 19
  18. 18.What is the 17th term of the AP 16, 22, 28, 34, …? (a) 112 (b) 102 (c) 118 (d) 96
  19. 19.What is the 40th term of the AP 17, 23, 29, 35, …? (a) 257 (b) 251 (c) 234 (d) 240
  20. 20.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 169 (d) 182
  21. 21.What is the 29th term of the AP 3, 8, 13, 18, …? (a) 140 (b) 143 (c) 145 (d) 148
  22. 22.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2592 (c) 2628 (d) 2556
  23. 23.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 676 (d) 51
  24. 24.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 256 (d) 136
  25. 25.What is the 23rd term of the AP 1, 10, 19, 28, …? (a) 198 (b) 207 (c) 199 (d) 208
  26. 26.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 154 (d) 136
  27. 27.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4371 (c) 4465 (d) 4418
  28. 28.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 22 (b) 144 (c) 72 (d) 84
  29. 29.Which term of the AP 4, 13, 22, 31, … is 283? (a) 32nd (b) 31st (c) 34th (d) 33rd
  30. 30.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 102 (b) 60 (c) 51 (d) 16
  31. 31.What is the 30th term of the AP 3, 12, 21, 30, …? (a) 270 (b) 273 (c) 261 (d) 264
  32. 32.What is the 13th term of the AP 2, 8, 14, 20, …? (a) 74 (b) 78 (c) 72 (d) 80
  33. 33.Which term of the AP 9, 15, 21, 27, … is 219? (a) 38th (b) 36th (c) 35th (d) 37th
  34. 34.What is the 20th term of the AP 1, 3, 5, 7, …? (a) 38 (b) 39 (c) 40 (d) 41
  35. 35.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 17 (b) 16 (c) 20 (d) 18
  36. 36.Which term of the AP 7, 10, 13, 16, … is 43? (a) 12th (b) 15th (c) 13th (d) 14th
  37. 37.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 72 (c) 80 (d) 16
  38. 38.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 162 (b) 19 (c) 324 (d) 168
  39. 39.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 36 (b) 147 (c) 152 (d) 294
  40. 40.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 22 (b) 128 (c) 120 (d) 240

Answer key

  1. 83
  2. 946
  3. 65
  4. 36th
  5. 12
  6. 299
  7. 30th
  8. 91
  9. 57
  10. 235
  11. 140
  12. 114
  13. 28th
  14. 220
  15. 900
  16. 277
  17. 19
  18. 112
  19. 251
  20. 169
  21. 143
  22. 2628
  23. 676
  24. 256
  25. 199
  26. 153
  27. 4465
  28. 72
  29. 32nd
  30. 51
  31. 264
  32. 74
  33. 36th
  34. 39
  35. 17
  36. 13th
  37. 72
  38. 162
  39. 147
  40. 120

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