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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 508 · 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 17? (a) 306 (b) 136 (c) 154 (d) 153
  2. 2.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 29 (b) 160 (c) 148 (d) 296
  3. 3.Which term of the AP 4, 11, 18, 25, … is 151? (a) 22nd (b) 21st (c) 23rd (d) 24th
  4. 4.What is the 27th term of the AP 9, 18, 27, 36, …? (a) 252 (b) 234 (c) 244 (d) 243
  5. 5.What is the 25th term of the AP 3, 8, 13, 18, …? (a) 123 (b) 120 (c) 125 (d) 128
  6. 6.What is the sum of all the whole numbers from 1 to 76? (a) 2926 (b) 5852 (c) 2850 (d) 2888
  7. 7.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 72 (b) 128 (c) 64 (d) 15
  8. 8.What is the 39th term of the AP 15, 21, 27, 33, …? (a) 234 (b) 228 (c) 249 (d) 243
  9. 9.Which term of the AP 18, 25, 32, 39, … is 235? (a) 33rd (b) 34th (c) 32nd (d) 31st
  10. 10.What is the 16th term of the AP 18, 21, 24, 27, …? (a) 45 (b) 66 (c) 63 (d) 48
  11. 11.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 2926 (c) 6006 (d) 3003
  12. 12.What is the 36th term of the AP 10, 15, 20, 25, …? (a) 190 (b) 180 (c) 175 (d) 185
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  14. 14.What is the 31st term of the AP 18, 20, 22, 24, …? (a) 62 (b) 60 (c) 78 (d) 80
  15. 15.Which term of the AP 8, 17, 26, 35, … is 251? (a) 27th (b) 30th (c) 29th (d) 28th
  16. 16.What is the missing term in the AP 16, 21, 26, ?, 36? (a) 31 (b) 30 (c) 32 (d) 36
  17. 17.What is the 35th term of the AP 11, 20, 29, 38, …? (a) 326 (b) 317 (c) 306 (d) 315
  18. 18.Which term of the AP 9, 18, 27, 36, … is 252? (a) 30th (b) 28th (c) 29th (d) 27th
  19. 19.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 43 (b) 506 (c) 253 (d) 275
  20. 20.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 210 (c) 105 (d) 24
  21. 21.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 17 (b) 15 (c) 25 (d) 16
  22. 22.What is the 18th term of the AP 4, 10, 16, 22, …? (a) 102 (b) 108 (c) 112 (d) 106
  23. 23.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 703 (c) 741 (d) 1482
  24. 24.What is the 26th term of the AP 13, 18, 23, 28, …? (a) 130 (b) 138 (c) 125 (d) 143
  25. 25.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 1035 (d) 2070
  26. 26.What is the 16th term of the AP 4, 6, 8, 10, …? (a) 34 (b) 32 (c) 36 (d) 30
  27. 27.What is the 27th term of the AP 17, 26, 35, 44, …? (a) 243 (b) 234 (c) 251 (d) 260
  28. 28.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 528 (b) 984 (c) 74 (d) 492
  29. 29.Which term of the AP 2, 6, 10, 14, … is 70? (a) 20th (b) 19th (c) 18th (d) 17th
  30. 30.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 18 (b) 14 (c) 13 (d) 15
  31. 31.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 240 (c) 120 (d) 121
  32. 32.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2346 (c) 2312 (d) 2278
  33. 33.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 130 (b) 19 (c) 68 (d) 65
  34. 34.What is the 22nd term of the AP 6, 9, 12, 15, …? (a) 66 (b) 63 (c) 69 (d) 72
  35. 35.What is the 11th term of the AP 11, 14, 17, 20, …? (a) 41 (b) 44 (c) 33 (d) 30
  36. 36.What is the 11th term of the AP 6, 15, 24, 33, …? (a) 96 (b) 99 (c) 105 (d) 90
  37. 37.What is the 18th term of the AP 12, 17, 22, 27, …? (a) 85 (b) 90 (c) 102 (d) 97
  38. 38.What is the 18th term of the AP 16, 18, 20, 22, …? (a) 34 (b) 36 (c) 50 (d) 52
  39. 39.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 13 (b) 17 (c) 14 (d) 15
  40. 40.What is the sum of all the whole numbers from 1 to 74? (a) 5550 (b) 2701 (c) 2738 (d) 2775

Answer key

  1. 153
  2. 148
  3. 22nd
  4. 243
  5. 123
  6. 2926
  7. 64
  8. 243
  9. 32nd
  10. 63
  11. 3003
  12. 185
  13. 900
  14. 78
  15. 28th
  16. 31
  17. 317
  18. 28th
  19. 253
  20. 105
  21. 16
  22. 106
  23. 741
  24. 138
  25. 1035
  26. 34
  27. 251
  28. 492
  29. 18th
  30. 14
  31. 120
  32. 2346
  33. 65
  34. 69
  35. 41
  36. 96
  37. 97
  38. 50
  39. 14
  40. 2775

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