← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 41 · 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 6 terms of the AP 7, 13, 19, …? (a) 132 (b) 150 (c) 37 (d) 264
  2. 2.Which term of the AP 20, 23, 26, 29, … is 47? (a) 12th (b) 11th (c) 10th (d) 9th
  3. 3.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 45 (b) 384 (c) 192 (d) 216
  4. 4.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 308 (b) 34 (c) 168 (d) 154
  5. 5.What is the 24th term of the AP 20, 25, 30, 35, …? (a) 140 (b) 120 (c) 135 (d) 115
  6. 6.What is the 32nd term of the AP 19, 21, 23, 25, …? (a) 62 (b) 64 (c) 83 (d) 81
  7. 7.What is the missing term in the AP 17, 21, 25, ?, 33? (a) 30 (b) 28 (c) 33 (d) 29
  8. 8.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 31 (b) 30 (c) 39 (d) 32
  9. 9.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 36 (b) 35 (c) 45 (d) 37
  10. 10.What is the 18th term of the AP 11, 18, 25, 32, …? (a) 130 (b) 119 (c) 126 (d) 137
  11. 11.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 90 (b) 85 (c) 170 (d) 27
  12. 12.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 147 (b) 33 (c) 161 (d) 294
  13. 13.What is the 15th term of the AP 19, 21, 23, 25, …? (a) 28 (b) 30 (c) 47 (d) 49
  14. 14.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 684 (b) 342 (c) 56 (d) 372
  15. 15.What is the 26th term of the AP 16, 25, 34, 43, …? (a) 241 (b) 225 (c) 250 (d) 234
  16. 16.What is the missing term in the AP 9, 17, 25, ?, 41? (a) 34 (b) 33 (c) 32 (d) 41
  17. 17.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 57 (d) 435
  18. 18.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 52 (b) 104 (c) 10 (d) 56
  19. 19.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 19 (b) 18 (c) 20 (d) 25
  20. 20.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 7140 (c) 3486 (d) 3570
  21. 21.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 35 (d) 171
  22. 22.What is the 23rd term of the AP 11, 20, 29, 38, …? (a) 198 (b) 207 (c) 209 (d) 218
  23. 23.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 33 (b) 195 (c) 210 (d) 390
  24. 24.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 40 (c) 10 (d) 41
  25. 25.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 41 (b) 35 (c) 36 (d) 34
  26. 26.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 31 (b) 24 (c) 22 (d) 23
  27. 27.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 682 (c) 341 (d) 56
  28. 28.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 110 (b) 13 (c) 55 (d) 56
  29. 29.What is the 17th term of the AP 19, 22, 25, 28, …? (a) 51 (b) 70 (c) 67 (d) 48
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 144 (d) 156
  31. 31.What is the 25th term of the AP 19, 21, 23, 25, …? (a) 48 (b) 67 (c) 69 (d) 50
  32. 32.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1653 (c) 1711 (d) 1682
  33. 33.What is the 19th term of the AP 8, 17, 26, 35, …? (a) 170 (b) 162 (c) 179 (d) 171
  34. 34.What is the 32nd term of the AP 17, 21, 25, 29, …? (a) 124 (b) 145 (c) 141 (d) 128
  35. 35.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 37 (b) 38 (c) 47 (d) 39
  36. 36.What is the 30th term of the AP 5, 12, 19, 26, …? (a) 203 (b) 210 (c) 215 (d) 208
  37. 37.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 64 (b) 407 (c) 374 (d) 748
  38. 38.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 17 (b) 18 (c) 19 (d) 24
  39. 39.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 29 (d) 225
  40. 40.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 42 (b) 260 (c) 480 (d) 240

Answer key

  1. 132
  2. 10th
  3. 192
  4. 154
  5. 135
  6. 81
  7. 29
  8. 31
  9. 36
  10. 130
  11. 85
  12. 147
  13. 47
  14. 342
  15. 241
  16. 33
  17. 841
  18. 52
  19. 19
  20. 3570
  21. 324
  22. 209
  23. 195
  24. 40
  25. 35
  26. 23
  27. 341
  28. 55
  29. 67
  30. 144
  31. 67
  32. 1711
  33. 170
  34. 141
  35. 38
  36. 208
  37. 374
  38. 18
  39. 225
  40. 240

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