← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 568 · 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 20, 23, 26, 29, … is 104? (a) 30th (b) 28th (c) 31st (d) 29th
  2. 2.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 36 (b) 240 (c) 225 (d) 450
  3. 3.What is the 40th term of the AP 5, 12, 19, 26, …? (a) 285 (b) 280 (c) 278 (d) 273
  4. 4.What is the 38th term of the AP 1, 5, 9, 13, …? (a) 148 (b) 149 (c) 153 (d) 152
  5. 5.What is the 15th term of the AP 16, 22, 28, 34, …? (a) 84 (b) 106 (c) 100 (d) 90
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  7. 7.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 34 (b) 212 (c) 418 (d) 209
  8. 8.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 31 (b) 133 (c) 147 (d) 266
  9. 9.What is the 23rd term of the AP 16, 22, 28, 34, …? (a) 148 (b) 138 (c) 154 (d) 132
  10. 10.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 114 (b) 198 (c) 29 (d) 99
  11. 11.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 120 (b) 14 (c) 61 (d) 60
  12. 12.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 105 (b) 210 (c) 108 (d) 24
  13. 13.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 29 (b) 23 (c) 22 (d) 24
  14. 14.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1892 (c) 3782 (d) 1891
  15. 15.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1485 (c) 2970 (d) 1458
  16. 16.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 27 (b) 21 (c) 20 (d) 22
  17. 17.Which term of the AP 10, 14, 18, 22, … is 122? (a) 30th (b) 28th (c) 31st (d) 29th
  18. 18.What is the 24th term of the AP 5, 10, 15, 20, …? (a) 120 (b) 121 (c) 125 (d) 115
  19. 19.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 336 (b) 50 (c) 672 (d) 360
  20. 20.What is the 15th term of the AP 15, 22, 29, 36, …? (a) 98 (b) 105 (c) 120 (d) 113
  21. 21.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 72 (d) 64
  22. 22.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 610 (b) 305 (c) 53 (d) 330
  23. 23.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 702 (c) 325 (d) 338
  24. 24.What is the 39th term of the AP 11, 14, 17, 20, …? (a) 117 (b) 128 (c) 114 (d) 125
  25. 25.What is the 40th term of the AP 10, 12, 14, 16, …? (a) 80 (b) 88 (c) 90 (d) 78
  26. 26.What is the 32nd term of the AP 9, 17, 25, 33, …? (a) 248 (b) 265 (c) 256 (d) 257
  27. 27.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 946 (c) 1892 (d) 903
  28. 28.Which term of the AP 10, 12, 14, 16, … is 32? (a) 16th (b) 13th (c) 11th (d) 12th
  29. 29.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 114 (b) 228 (c) 29 (d) 126
  30. 30.What is the missing term in the AP 1, 10, ?, 28, 37? (a) 28 (b) 20 (c) 19 (d) 18
  31. 31.Which term of the AP 19, 22, 25, 28, … is 52? (a) 14th (b) 13th (c) 12th (d) 11th
  32. 32.What is the 23rd term of the AP 20, 24, 28, 32, …? (a) 92 (b) 112 (c) 88 (d) 108
  33. 33.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 144 (b) 276 (c) 17 (d) 138
  34. 34.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 144 (b) 288 (c) 24 (d) 153
  35. 35.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 19 (c) 108 (d) 198
  36. 36.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3486 (c) 3528 (d) 3570
  37. 37.Which term of the AP 3, 6, 9, 12, … is 105? (a) 36th (b) 37th (c) 35th (d) 34th
  38. 38.What is the 38th term of the AP 3, 7, 11, 15, …? (a) 152 (b) 151 (c) 148 (d) 155
  39. 39.What is the sum of all the whole numbers from 1 to 41? (a) 862 (b) 1722 (c) 820 (d) 861
  40. 40.What is the 16th term of the AP 20, 24, 28, 32, …? (a) 80 (b) 84 (c) 60 (d) 64

Answer key

  1. 29th
  2. 225
  3. 278
  4. 149
  5. 100
  6. 25
  7. 209
  8. 133
  9. 148
  10. 99
  11. 60
  12. 105
  13. 23
  14. 1891
  15. 1485
  16. 21
  17. 29th
  18. 120
  19. 336
  20. 113
  21. 64
  22. 305
  23. 351
  24. 125
  25. 88
  26. 257
  27. 946
  28. 12th
  29. 114
  30. 19
  31. 12th
  32. 108
  33. 138
  34. 144
  35. 99
  36. 3570
  37. 35th
  38. 151
  39. 861
  40. 80

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