← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 36 · 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 24th term of the AP 13, 17, 21, 25, …? (a) 105 (b) 92 (c) 96 (d) 109
  2. 2.What is the missing term in the AP 16, 18, 20, ?, 24? (a) 23 (b) 22 (c) 24 (d) 21
  3. 3.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 4754 (c) 9506 (d) 4656
  4. 4.Which term of the AP 16, 19, 22, 25, … is 49? (a) 12th (b) 14th (c) 13th (d) 11th
  5. 5.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 73 (b) 960 (c) 516 (d) 480
  6. 6.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 16 (b) 200 (c) 100 (d) 104
  7. 7.What is the 10th term of the AP 2, 11, 20, 29, …? (a) 92 (b) 83 (c) 81 (d) 90
  8. 8.What is the 13th term of the AP 2, 4, 6, 8, …? (a) 26 (b) 27 (c) 24 (d) 28
  9. 9.What is the 30th term of the AP 9, 12, 15, 18, …? (a) 90 (b) 96 (c) 87 (d) 99
  10. 10.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 277 (c) 552 (d) 276
  11. 11.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 51 (b) 310 (c) 285 (d) 570
  12. 12.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2145 (c) 2178 (d) 2211
  13. 13.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 702 (d) 351
  14. 14.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4951 (c) 4950 (d) 4851
  15. 15.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 150 (b) 20 (c) 84 (d) 75
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  17. 17.What is the 31st term of the AP 18, 23, 28, 33, …? (a) 150 (b) 173 (c) 168 (d) 155
  18. 18.What is the 17th term of the AP 11, 20, 29, 38, …? (a) 155 (b) 164 (c) 144 (d) 153
  19. 19.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 342 (d) 171
  20. 20.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 44 (b) 37 (c) 38 (d) 39
  21. 21.What is the 32nd term of the AP 16, 24, 32, 40, …? (a) 272 (b) 256 (c) 248 (d) 264
  22. 22.What is the 15th term of the AP 14, 18, 22, 26, …? (a) 74 (b) 70 (c) 56 (d) 60
  23. 23.What is the missing term in the AP 12, 15, ?, 21, 24? (a) 17 (b) 18 (c) 19 (d) 21
  24. 24.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 17 (b) 15 (c) 22 (d) 16
  25. 25.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 60 (b) 120 (c) 11 (d) 64
  26. 26.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 210 (c) 98 (d) 91
  27. 27.What is the 16th term of the AP 11, 18, 25, 32, …? (a) 105 (b) 116 (c) 123 (d) 112
  28. 28.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 22 (b) 264 (c) 132 (d) 143
  29. 29.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 130 (b) 19 (c) 68 (d) 65
  30. 30.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4560 (c) 4561 (d) 4465
  31. 31.What is the sum of all the whole numbers from 1 to 21? (a) 462 (b) 231 (c) 232 (d) 210
  32. 32.What is the 30th term of the AP 18, 27, 36, 45, …? (a) 288 (b) 261 (c) 279 (d) 270
  33. 33.What is the 14th term of the AP 12, 20, 28, 36, …? (a) 124 (b) 112 (c) 104 (d) 116
  34. 34.Which term of the AP 9, 16, 23, 30, … is 93? (a) 15th (b) 13th (c) 12th (d) 14th
  35. 35.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 3080 (c) 1540 (d) 1485
  36. 36.What is the 35th term of the AP 11, 13, 15, 17, …? (a) 68 (b) 79 (c) 70 (d) 81
  37. 37.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 9 (b) 7 (c) 8 (d) 15
  38. 38.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 51 (b) 348 (c) 372 (d) 696
  39. 39.What is the missing term in the AP 20, ?, 36, 44, 52? (a) 27 (b) 36 (c) 29 (d) 28
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 21 (d) 42

Answer key

  1. 105
  2. 22
  3. 4753
  4. 12th
  5. 480
  6. 100
  7. 83
  8. 26
  9. 96
  10. 276
  11. 285
  12. 2211
  13. 351
  14. 4950
  15. 75
  16. 64
  17. 168
  18. 155
  19. 324
  20. 38
  21. 264
  22. 70
  23. 18
  24. 16
  25. 60
  26. 105
  27. 116
  28. 132
  29. 65
  30. 4560
  31. 231
  32. 279
  33. 116
  34. 13th
  35. 1540
  36. 79
  37. 8
  38. 348
  39. 28
  40. 36

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