← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 824 · 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 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 72 (d) 64
  2. 2.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1485 (c) 1458 (d) 2970
  3. 3.What is the 32nd term of the AP 16, 21, 26, 31, …? (a) 155 (b) 160 (c) 176 (d) 171
  4. 4.What is the 30th term of the AP 14, 18, 22, 26, …? (a) 134 (b) 116 (c) 120 (d) 130
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  6. 6.What is the 13th term of the AP 7, 11, 15, 19, …? (a) 59 (b) 55 (c) 48 (d) 52
  7. 7.What is the 13th term of the AP 1, 10, 19, 28, …? (a) 118 (b) 109 (c) 108 (d) 117
  8. 8.Which term of the AP 2, 11, 20, 29, … is 281? (a) 34th (b) 31st (c) 32nd (d) 33rd
  9. 9.What is the 13th term of the AP 10, 17, 24, 31, …? (a) 101 (b) 84 (c) 91 (d) 94
  10. 10.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 22 (c) 182 (d) 94
  11. 11.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 180 (b) 25 (c) 168 (d) 336
  12. 12.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 9506 (c) 4753 (d) 4656
  13. 13.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 2850 (c) 5700 (d) 2775
  14. 14.What is the 16th term of the AP 8, 15, 22, 29, …? (a) 112 (b) 113 (c) 105 (d) 120
  15. 15.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 781 (d) 780
  16. 16.What is the 29th term of the AP 11, 17, 23, 29, …? (a) 185 (b) 174 (c) 168 (d) 179
  17. 17.What is the 10th term of the AP 4, 9, 14, 19, …? (a) 54 (b) 50 (c) 45 (d) 49
  18. 18.What is the 36th term of the AP 3, 10, 17, 24, …? (a) 248 (b) 245 (c) 255 (d) 252
  19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  20. 20.Which term of the AP 13, 18, 23, 28, … is 93? (a) 18th (b) 19th (c) 16th (d) 17th
  21. 21.What is the 30th term of the AP 1, 10, 19, 28, …? (a) 270 (b) 261 (c) 262 (d) 271
  22. 22.What is the 40th term of the AP 4, 11, 18, 25, …? (a) 273 (b) 277 (c) 284 (d) 280
  23. 23.What is the missing term in the AP 4, 13, ?, 31, 40? (a) 31 (b) 21 (c) 22 (d) 23
  24. 24.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 46 (b) 392 (c) 217 (d) 196
  25. 25.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 841 (d) 870
  26. 26.What is the missing term in the AP 14, ?, 24, 29, 34? (a) 24 (b) 20 (c) 19 (d) 18
  27. 27.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 56 (c) 341 (d) 682
  28. 28.Which term of the AP 17, 25, 33, 41, … is 153? (a) 19th (b) 20th (c) 17th (d) 18th
  29. 29.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 140 (b) 126 (c) 30 (d) 252
  30. 30.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 143 (b) 144 (c) 286 (d) 18
  31. 31.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 58 (b) 55 (c) 110 (d) 17
  32. 32.Which term of the AP 1, 4, 7, 10, … is 52? (a) 18th (b) 19th (c) 20th (d) 17th
  33. 33.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 18 (b) 252 (c) 127 (d) 126
  34. 34.What is the 11th term of the AP 18, 25, 32, 39, …? (a) 95 (b) 88 (c) 77 (d) 70
  35. 35.What is the 13th term of the AP 3, 7, 11, 15, …? (a) 48 (b) 55 (c) 51 (d) 52
  36. 36.Which term of the AP 14, 18, 22, 26, … is 46? (a) 8th (b) 9th (c) 11th (d) 10th
  37. 37.What is the 13th term of the AP 18, 25, 32, 39, …? (a) 91 (b) 84 (c) 109 (d) 102
  38. 38.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 703 (c) 741 (d) 1482
  39. 39.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 3698 (c) 7482 (d) 3655
  40. 40.What is the 39th term of the AP 1, 8, 15, 22, …? (a) 273 (b) 266 (c) 267 (d) 274

Answer key

  1. 64
  2. 1485
  3. 171
  4. 130
  5. 49
  6. 55
  7. 109
  8. 32nd
  9. 94
  10. 91
  11. 168
  12. 4753
  13. 2850
  14. 113
  15. 780
  16. 179
  17. 49
  18. 248
  19. 400
  20. 17th
  21. 262
  22. 277
  23. 22
  24. 196
  25. 841
  26. 19
  27. 341
  28. 18th
  29. 126
  30. 143
  31. 55
  32. 18th
  33. 126
  34. 88
  35. 51
  36. 9th
  37. 102
  38. 741
  39. 3741
  40. 267

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad