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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 6 · 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 87? (a) 3828 (b) 7656 (c) 3741 (d) 3829
  2. 2.Which term of the AP 5, 11, 17, 23, … is 119? (a) 22nd (b) 20th (c) 19th (d) 21st
  3. 3.Which term of the AP 7, 11, 15, 19, … is 115? (a) 28th (b) 30th (c) 29th (d) 27th
  4. 4.Which term of the AP 10, 14, 18, 22, … is 146? (a) 34th (b) 36th (c) 37th (d) 35th
  5. 5.What is the 12th term of the AP 2, 11, 20, 29, …? (a) 99 (b) 108 (c) 110 (d) 101
  6. 6.What is the 36th term of the AP 12, 14, 16, 18, …? (a) 70 (b) 84 (c) 72 (d) 82
  7. 7.What is the 32nd term of the AP 17, 25, 33, 41, …? (a) 265 (b) 248 (c) 273 (d) 256
  8. 8.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 240 (b) 51 (c) 264 (d) 480
  9. 9.What is the 25th term of the AP 9, 16, 23, 30, …? (a) 175 (b) 168 (c) 177 (d) 184
  10. 10.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 22 (b) 120 (c) 240 (d) 128
  11. 11.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 1953 (d) 2016
  12. 12.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 666 (c) 703 (d) 704
  13. 13.What is the 26th term of the AP 4, 7, 10, 13, …? (a) 79 (b) 75 (c) 82 (d) 78
  14. 14.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 496 (c) 497 (d) 992
  15. 15.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 56 (b) 98 (c) 49 (d) 13
  16. 16.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 372 (b) 56 (c) 684 (d) 342
  17. 17.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2557 (c) 2485 (d) 2556
  18. 18.What is the 34th term of the AP 16, 19, 22, 25, …? (a) 99 (b) 115 (c) 118 (d) 102
  19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 361 (c) 380 (d) 190
  20. 20.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 252 (b) 126 (c) 18 (d) 127
  21. 21.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 280 (b) 260 (c) 44 (d) 520
  22. 22.What is the sum of all the whole numbers from 1 to 28? (a) 406 (b) 392 (c) 812 (d) 378
  23. 23.What is the 18th term of the AP 12, 17, 22, 27, …? (a) 90 (b) 102 (c) 85 (d) 97
  24. 24.What is the 20th term of the AP 16, 21, 26, 31, …? (a) 100 (b) 111 (c) 116 (d) 95
  25. 25.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2702 (c) 2701 (d) 5402
  26. 26.Which term of the AP 3, 10, 17, 24, … is 262? (a) 38th (b) 39th (c) 40th (d) 37th
  27. 27.What is the 32nd term of the AP 5, 11, 17, 23, …? (a) 191 (b) 197 (c) 186 (d) 192
  28. 28.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 72 (c) 12 (d) 73
  29. 29.What is the 38th term of the AP 10, 17, 24, 31, …? (a) 266 (b) 276 (c) 259 (d) 269
  30. 30.What is the missing term in the AP 19, 23, ?, 31, 35? (a) 28 (b) 26 (c) 27 (d) 31
  31. 31.What is the 35th term of the AP 17, 22, 27, 32, …? (a) 192 (b) 187 (c) 175 (d) 170
  32. 32.What is the missing term in the AP 9, 15, 21, ?, 33? (a) 28 (b) 26 (c) 33 (d) 27
  33. 33.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 120 (c) 240 (d) 121
  34. 34.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 57 (d) 435
  35. 35.What is the 35th term of the AP 3, 7, 11, 15, …? (a) 140 (b) 139 (c) 136 (d) 143
  36. 36.What is the 29th term of the AP 11, 14, 17, 20, …? (a) 84 (b) 95 (c) 98 (d) 87
  37. 37.What is the 18th term of the AP 10, 19, 28, 37, …? (a) 163 (b) 172 (c) 162 (d) 153
  38. 38.What is the 28th term of the AP 12, 20, 28, 36, …? (a) 236 (b) 228 (c) 216 (d) 224
  39. 39.Which term of the AP 11, 18, 25, 32, … is 242? (a) 36th (b) 34th (c) 33rd (d) 35th
  40. 40.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9

Answer key

  1. 3828
  2. 20th
  3. 28th
  4. 35th
  5. 101
  6. 82
  7. 265
  8. 240
  9. 177
  10. 120
  11. 2016
  12. 703
  13. 79
  14. 496
  15. 49
  16. 342
  17. 2556
  18. 115
  19. 361
  20. 126
  21. 260
  22. 406
  23. 97
  24. 111
  25. 2701
  26. 38th
  27. 191
  28. 72
  29. 269
  30. 27
  31. 187
  32. 27
  33. 120
  34. 841
  35. 139
  36. 95
  37. 163
  38. 228
  39. 34th
  40. 25

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