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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 239 · 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.Which term of the AP 7, 10, 13, 16, … is 124? (a) 39th (b) 40th (c) 42nd (d) 41st
  2. 2.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 4692 (c) 2312 (d) 2346
  3. 3.Which term of the AP 3, 5, 7, 9, … is 25? (a) 14th (b) 11th (c) 13th (d) 12th
  4. 4.Which term of the AP 14, 18, 22, 26, … is 106? (a) 25th (b) 23rd (c) 24th (d) 26th
  5. 5.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 78 (b) 84 (c) 18 (d) 156
  6. 6.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 351 (d) 702
  7. 7.Which term of the AP 12, 17, 22, 27, … is 52? (a) 9th (b) 8th (c) 10th (d) 11th
  8. 8.What is the 27th term of the AP 10, 13, 16, 19, …? (a) 81 (b) 88 (c) 78 (d) 91
  9. 9.What is the 36th term of the AP 18, 21, 24, 27, …? (a) 126 (b) 105 (c) 123 (d) 108
  10. 10.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 15 (b) 17 (c) 16 (d) 24
  11. 11.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 380 (c) 191 (d) 171
  12. 12.What is the missing term in the AP 14, 21, ?, 35, 42? (a) 35 (b) 28 (c) 29 (d) 27
  13. 13.What is the 30th term of the AP 6, 13, 20, 27, …? (a) 216 (b) 210 (c) 203 (d) 209
  14. 14.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 384 (b) 354 (c) 57 (d) 708
  15. 15.Which term of the AP 5, 7, 9, 11, … is 53? (a) 26th (b) 27th (c) 25th (d) 24th
  16. 16.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 40 (b) 234 (c) 432 (d) 216
  17. 17.What is the 14th term of the AP 7, 15, 23, 31, …? (a) 119 (b) 111 (c) 104 (d) 112
  18. 18.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 3192 (c) 1568 (d) 1596
  19. 19.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 390 (b) 385 (c) 770 (d) 60
  20. 20.Which term of the AP 5, 11, 17, 23, … is 53? (a) 10th (b) 11th (c) 8th (d) 9th
  21. 21.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 1036 (c) 2070 (d) 990
  22. 22.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 319 (b) 47 (c) 297 (d) 594
  23. 23.Which term of the AP 4, 7, 10, 13, … is 25? (a) 9th (b) 8th (c) 7th (d) 10th
  24. 24.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 17 (b) 132 (c) 133 (d) 264
  25. 25.Which term of the AP 4, 7, 10, 13, … is 52? (a) 16th (b) 18th (c) 19th (d) 17th
  26. 26.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 6162 (c) 3081 (d) 3003
  27. 27.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 7656 (c) 3741 (d) 3829
  28. 28.What is the 28th term of the AP 19, 23, 27, 31, …? (a) 112 (b) 131 (c) 127 (d) 108
  29. 29.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 9506 (c) 4656 (d) 4754
  30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
  31. 31.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 13 (b) 12 (c) 11 (d) 16
  32. 32.What is the 37th term of the AP 4, 6, 8, 10, …? (a) 74 (b) 72 (c) 78 (d) 76
  33. 33.Which term of the AP 7, 15, 23, 31, … is 231? (a) 30th (b) 29th (c) 31st (d) 28th
  34. 34.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 150 (b) 15 (c) 75 (d) 78
  35. 35.What is the 13th term of the AP 14, 17, 20, 23, …? (a) 36 (b) 53 (c) 39 (d) 50
  36. 36.Which term of the AP 12, 19, 26, 33, … is 201? (a) 30th (b) 28th (c) 27th (d) 29th
  37. 37.Which term of the AP 12, 20, 28, 36, … is 268? (a) 32nd (b) 34th (c) 33rd (d) 35th
  38. 38.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 60 (c) 100 (d) 50
  39. 39.Which term of the AP 16, 25, 34, 43, … is 277? (a) 32nd (b) 29th (c) 30th (d) 31st
  40. 40.What is the 33rd term of the AP 15, 21, 27, 33, …? (a) 207 (b) 192 (c) 213 (d) 198

Answer key

  1. 40th
  2. 2346
  3. 12th
  4. 24th
  5. 78
  6. 676
  7. 9th
  8. 88
  9. 123
  10. 16
  11. 190
  12. 28
  13. 209
  14. 354
  15. 25th
  16. 216
  17. 111
  18. 1596
  19. 385
  20. 9th
  21. 1035
  22. 297
  23. 8th
  24. 132
  25. 17th
  26. 3081
  27. 3828
  28. 127
  29. 4753
  30. 324
  31. 12
  32. 76
  33. 29th
  34. 75
  35. 50
  36. 28th
  37. 33rd
  38. 50
  39. 30th
  40. 207

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