← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 851 · 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 missing term in the AP 4, ?, 10, 13, 16? (a) 10 (b) 6 (c) 7 (d) 8
  2. 2.Which term of the AP 9, 17, 25, 33, … is 289? (a) 37th (b) 35th (c) 38th (d) 36th
  3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 406 (c) 55 (d) 784
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 105 (c) 27 (d) 196
  5. 5.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 864 (b) 69 (c) 468 (d) 432
  6. 6.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 180 (b) 27 (c) 190 (d) 360
  7. 7.What is the missing term in the AP 2, 9, 16, ?, 30? (a) 30 (b) 22 (c) 24 (d) 23
  8. 8.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 300 (b) 560 (c) 46 (d) 280
  9. 9.Which term of the AP 19, 24, 29, 34, … is 169? (a) 31st (b) 30th (c) 33rd (d) 32nd
  10. 10.What is the missing term in the AP 6, 9, ?, 15, 18? (a) 13 (b) 15 (c) 12 (d) 11
  11. 11.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 90 (b) 48 (c) 45 (d) 15
  12. 12.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 120 (c) 29 (d) 240
  13. 13.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
  14. 14.What is the 13th term of the AP 13, 22, 31, 40, …? (a) 121 (b) 130 (c) 117 (d) 108
  15. 15.What is the 34th term of the AP 12, 16, 20, 24, …? (a) 132 (b) 144 (c) 148 (d) 136
  16. 16.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 4371 (c) 8742 (d) 4278
  17. 17.What is the 16th term of the AP 4, 13, 22, 31, …? (a) 148 (b) 135 (c) 139 (d) 144
  18. 18.What is the 12th term of the AP 13, 16, 19, 22, …? (a) 36 (b) 46 (c) 33 (d) 49
  19. 19.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 44 (b) 208 (c) 368 (d) 184
  20. 20.What is the 37th term of the AP 12, 15, 18, 21, …? (a) 108 (b) 111 (c) 123 (d) 120
  21. 21.What is the 40th term of the AP 3, 8, 13, 18, …? (a) 200 (b) 203 (c) 198 (d) 195
  22. 22.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 35 (d) 342
  23. 23.What is the 36th term of the AP 14, 16, 18, 20, …? (a) 70 (b) 72 (c) 86 (d) 84
  24. 24.Which term of the AP 4, 12, 20, 28, … is 100? (a) 14th (b) 13th (c) 15th (d) 12th
  25. 25.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 379 (c) 756 (d) 351
  26. 26.What is the 40th term of the AP 16, 21, 26, 31, …? (a) 211 (b) 195 (c) 216 (d) 200
  27. 27.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 23 (b) 22 (c) 24 (d) 29
  28. 28.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 506 (c) 253 (d) 242
  29. 29.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 366 (b) 58 (c) 732 (d) 396
  30. 30.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 80 (b) 43 (c) 40 (d) 14
  31. 31.What is the 16th term of the AP 7, 16, 25, 34, …? (a) 144 (b) 151 (c) 135 (d) 142
  32. 32.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 230 (b) 115 (c) 16 (d) 120
  33. 33.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 14 (b) 99 (c) 100 (d) 198
  34. 34.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 70 (b) 63 (c) 15 (d) 126
  35. 35.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 360 (b) 330 (c) 660 (d) 60
  36. 36.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 105 (c) 210 (d) 98
  37. 37.What is the 14th term of the AP 9, 11, 13, 15, …? (a) 28 (b) 37 (c) 26 (d) 35
  38. 38.What is the 32nd term of the AP 18, 24, 30, 36, …? (a) 204 (b) 186 (c) 192 (d) 210
  39. 39.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 140 (b) 18 (c) 75 (d) 70
  40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121

Answer key

  1. 7
  2. 36th
  3. 784
  4. 196
  5. 432
  6. 180
  7. 23
  8. 280
  9. 31st
  10. 12
  11. 45
  12. 225
  13. 441
  14. 121
  15. 144
  16. 4371
  17. 139
  18. 46
  19. 184
  20. 120
  21. 198
  22. 324
  23. 84
  24. 13th
  25. 378
  26. 211
  27. 23
  28. 253
  29. 366
  30. 40
  31. 142
  32. 115
  33. 99
  34. 63
  35. 330
  36. 105
  37. 35
  38. 204
  39. 70
  40. 121

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