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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 135 · 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 the first 7 terms of the AP 5, 11, 17, …? (a) 41 (b) 322 (c) 161 (d) 182
  2. 2.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
  3. 3.Which term of the AP 18, 20, 22, 24, … is 66? (a) 33rd (b) 26th (c) 25th (d) 24th
  4. 4.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 201 (b) 396 (c) 34 (d) 198
  5. 5.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 1332 (c) 648 (d) 630
  6. 6.What is the 29th term of the AP 19, 22, 25, 28, …? (a) 87 (b) 106 (c) 84 (d) 103
  7. 7.What is the 10th term of the AP 19, 21, 23, 25, …? (a) 37 (b) 20 (c) 39 (d) 18
  8. 8.What is the missing term in the AP 20, ?, 32, 38, 44? (a) 27 (b) 25 (c) 26 (d) 32
  9. 9.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 354 (c) 57 (d) 384
  10. 10.Which term of the AP 20, 24, 28, 32, … is 116? (a) 24th (b) 26th (c) 29th (d) 25th
  11. 11.Which term of the AP 12, 15, 18, 21, … is 33? (a) 7th (b) 8th (c) 11th (d) 9th
  12. 12.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 1653 (c) 3422 (d) 1711
  13. 13.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 38 (b) 32 (c) 30 (d) 31
  14. 14.What is the 30th term of the AP 15, 20, 25, 30, …? (a) 165 (b) 150 (c) 145 (d) 160
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
  16. 16.Which term of the AP 5, 7, 9, 11, … is 59? (a) 30th (b) 29th (c) 27th (d) 28th
  17. 17.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 12 (b) 73 (c) 72 (d) 144
  18. 18.What is the 35th term of the AP 4, 6, 8, 10, …? (a) 74 (b) 68 (c) 72 (d) 70
  19. 19.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3872 (c) 7832 (d) 3916
  20. 20.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 72 (b) 64 (c) 15 (d) 128
  21. 21.What is the 35th term of the AP 6, 15, 24, 33, …? (a) 315 (b) 306 (c) 321 (d) 312
  22. 22.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 66 (b) 132 (c) 21 (d) 78
  23. 23.What is the 37th term of the AP 3, 10, 17, 24, …? (a) 259 (b) 252 (c) 255 (d) 262
  24. 24.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 114 (c) 31 (d) 192
  25. 25.Which term of the AP 6, 12, 18, 24, … is 234? (a) 40th (b) 38th (c) 39th (d) 41st
  26. 26.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 176 (b) 96 (c) 18 (d) 88
  27. 27.Which term of the AP 19, 24, 29, 34, … is 124? (a) 22nd (b) 24th (c) 21st (d) 23rd
  28. 28.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 552 (c) 276 (d) 277
  29. 29.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 18 (b) 17 (c) 20 (d) 19
  30. 30.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 174 (b) 171 (c) 342 (d) 31
  31. 31.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 36 (b) 192 (c) 176 (d) 352
  32. 32.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1771 (c) 1711 (d) 1770
  33. 33.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 81 (d) 45
  34. 34.What is the missing term in the AP 20, ?, 36, 44, 52? (a) 29 (b) 27 (c) 36 (d) 28
  35. 35.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 414 (b) 444 (c) 62 (d) 828
  36. 36.What is the 12th term of the AP 17, 24, 31, 38, …? (a) 84 (b) 101 (c) 77 (d) 94
  37. 37.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 25 (b) 23 (c) 33 (d) 24
  38. 38.Which term of the AP 3, 5, 7, 9, … is 51? (a) 27th (b) 24th (c) 25th (d) 26th
  39. 39.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 2346 (c) 2278 (d) 4692
  40. 40.What is the 18th term of the AP 17, 26, 35, 44, …? (a) 153 (b) 179 (c) 162 (d) 170

Answer key

  1. 161
  2. 25
  3. 25th
  4. 198
  5. 666
  6. 103
  7. 37
  8. 26
  9. 354
  10. 25th
  11. 8th
  12. 1711
  13. 31
  14. 160
  15. 400
  16. 28th
  17. 72
  18. 72
  19. 3916
  20. 64
  21. 312
  22. 66
  23. 255
  24. 96
  25. 39th
  26. 88
  27. 22nd
  28. 276
  29. 18
  30. 171
  31. 176
  32. 1770
  33. 81
  34. 28
  35. 414
  36. 94
  37. 24
  38. 25th
  39. 2346
  40. 170

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