← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 412 · 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 15, 18, 21, 24, … is 51? (a) 12th (b) 14th (c) 17th (d) 13th
  2. 2.What is the missing term in the AP 10, 17, ?, 31, 38? (a) 25 (b) 31 (c) 23 (d) 24
  3. 3.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 210 (d) 420
  4. 4.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 702 (d) 51
  5. 5.What is the 21st term of the AP 15, 21, 27, 33, …? (a) 135 (b) 120 (c) 126 (d) 141
  6. 6.Which term of the AP 10, 18, 26, 34, … is 98? (a) 13th (b) 12th (c) 11th (d) 14th
  7. 7.What is the 36th term of the AP 15, 17, 19, 21, …? (a) 70 (b) 85 (c) 87 (d) 72
  8. 8.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 492 (b) 264 (c) 246 (d) 37
  9. 9.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 41 (d) 441
  10. 10.What is the 28th term of the AP 8, 12, 16, 20, …? (a) 120 (b) 116 (c) 108 (d) 112
  11. 11.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 212 (b) 418 (c) 34 (d) 209
  12. 12.What is the 29th term of the AP 19, 25, 31, 37, …? (a) 193 (b) 174 (c) 168 (d) 187
  13. 13.Which term of the AP 9, 11, 13, 15, … is 83? (a) 38th (b) 37th (c) 40th (d) 39th
  14. 14.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 171 (d) 342
  15. 15.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 19 (b) 20 (c) 18 (d) 25
  16. 16.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 187 (c) 374 (d) 27
  17. 17.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 30 (b) 29 (c) 31 (d) 34
  18. 18.What is the 29th term of the AP 11, 19, 27, 35, …? (a) 243 (b) 232 (c) 224 (d) 235
  19. 19.What is the 33rd term of the AP 15, 20, 25, 30, …? (a) 165 (b) 160 (c) 180 (d) 175
  20. 20.What is the 27th term of the AP 6, 9, 12, 15, …? (a) 87 (b) 81 (c) 84 (d) 78
  21. 21.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 38 (b) 39 (c) 46 (d) 40
  22. 22.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 10100 (c) 4950 (d) 5000
  23. 23.Which term of the AP 1, 5, 9, 13, … is 113? (a) 30th (b) 29th (c) 28th (d) 31st
  24. 24.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  25. 25.What is the 40th term of the AP 11, 18, 25, 32, …? (a) 280 (b) 284 (c) 291 (d) 273
  26. 26.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3570 (c) 3655 (d) 3656
  27. 27.What is the 16th term of the AP 6, 11, 16, 21, …? (a) 80 (b) 75 (c) 81 (d) 86
  28. 28.What is the 19th term of the AP 20, 23, 26, 29, …? (a) 74 (b) 57 (c) 54 (d) 77
  29. 29.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 7 (b) 27 (c) 54 (d) 30
  30. 30.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 43 (b) 207 (c) 414 (d) 212
  31. 31.What is the 20th term of the AP 4, 10, 16, 22, …? (a) 124 (b) 118 (c) 120 (d) 114
  32. 32.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 19 (b) 23 (c) 20 (d) 21
  33. 33.What is the 16th term of the AP 20, 22, 24, 26, …? (a) 30 (b) 32 (c) 50 (d) 52
  34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  35. 35.What is the 28th term of the AP 13, 22, 31, 40, …? (a) 265 (b) 256 (c) 252 (d) 243
  36. 36.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 37 (b) 242 (c) 484 (d) 245
  37. 37.Which term of the AP 1, 8, 15, 22, … is 99? (a) 17th (b) 15th (c) 16th (d) 14th
  38. 38.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 396 (b) 201 (c) 34 (d) 198
  39. 39.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 265 (b) 49 (c) 290 (d) 530
  40. 40.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 8930 (c) 4371 (d) 4418

Answer key

  1. 13th
  2. 24
  3. 400
  4. 676
  5. 135
  6. 12th
  7. 85
  8. 246
  9. 441
  10. 116
  11. 209
  12. 187
  13. 38th
  14. 324
  15. 19
  16. 187
  17. 30
  18. 235
  19. 175
  20. 84
  21. 39
  22. 5050
  23. 29th
  24. 289
  25. 284
  26. 3655
  27. 81
  28. 74
  29. 27
  30. 207
  31. 118
  32. 20
  33. 50
  34. 100
  35. 256
  36. 242
  37. 15th
  38. 198
  39. 265
  40. 4465

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