← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 3 · 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 11 terms of the AP 6, 12, 18, …? (a) 66 (b) 429 (c) 792 (d) 396
  2. 2.What is the 13th term of the AP 1, 3, 5, 7, …? (a) 24 (b) 26 (c) 27 (d) 25
  3. 3.What is the 36th term of the AP 20, 25, 30, 35, …? (a) 200 (b) 195 (c) 175 (d) 180
  4. 4.What is the 15th term of the AP 15, 19, 23, 27, …? (a) 71 (b) 56 (c) 60 (d) 75
  5. 5.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 225 (d) 29
  6. 6.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 279 (b) 558 (c) 306 (d) 55
  7. 7.What is the missing term in the AP 14, ?, 18, 20, 22? (a) 16 (b) 18 (c) 17 (d) 15
  8. 8.What is the 26th term of the AP 9, 13, 17, 21, …? (a) 113 (b) 100 (c) 104 (d) 109
  9. 9.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 51 (d) 351
  10. 10.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 28 (b) 147 (c) 288 (d) 144
  11. 11.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 252 (b) 49 (c) 450 (d) 225
  12. 12.What is the missing term in the AP 2, 10, ?, 26, 34? (a) 26 (b) 19 (c) 17 (d) 18
  13. 13.Which term of the AP 2, 5, 8, 11, … is 53? (a) 19th (b) 20th (c) 17th (d) 18th
  14. 14.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 56 (b) 112 (c) 14 (d) 63
  15. 15.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 4656 (c) 4608 (d) 9312
  16. 16.What is the 39th term of the AP 20, 28, 36, 44, …? (a) 312 (b) 304 (c) 324 (d) 332
  17. 17.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 114 (b) 96 (c) 31 (d) 192
  18. 18.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 10 (c) 90 (d) 45
  19. 19.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 378 (b) 41 (c) 189 (d) 194
  20. 20.What is the 11th term of the AP 5, 7, 9, 11, …? (a) 20 (b) 25 (c) 22 (d) 27
  21. 21.Which term of the AP 16, 23, 30, 37, … is 114? (a) 15th (b) 14th (c) 16th (d) 17th
  22. 22.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 198 (b) 108 (c) 99 (d) 19
  23. 23.Which term of the AP 20, 28, 36, 44, … is 212? (a) 27th (b) 25th (c) 26th (d) 24th
  24. 24.What is the 37th term of the AP 10, 14, 18, 22, …? (a) 144 (b) 154 (c) 158 (d) 148
  25. 25.What is the 10th term of the AP 5, 11, 17, 23, …? (a) 54 (b) 59 (c) 60 (d) 65
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
  27. 27.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 190 (d) 361
  28. 28.What is the 21st term of the AP 15, 17, 19, 21, …? (a) 42 (b) 57 (c) 55 (d) 40
  29. 29.What is the 10th term of the AP 19, 21, 23, 25, …? (a) 20 (b) 37 (c) 39 (d) 18
  30. 30.What is the 26th term of the AP 17, 25, 33, 41, …? (a) 225 (b) 200 (c) 208 (d) 217
  31. 31.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 102 (b) 14 (c) 204 (d) 108
  32. 32.Which term of the AP 18, 25, 32, 39, … is 158? (a) 20th (b) 22nd (c) 23rd (d) 21st
  33. 33.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 370 (c) 61 (d) 340
  34. 34.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 162 (b) 144 (c) 39 (d) 288
  35. 35.Which term of the AP 13, 17, 21, 25, … is 57? (a) 13th (b) 11th (c) 12th (d) 14th
  36. 36.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 300 (c) 325 (d) 650
  37. 37.Which term of the AP 6, 9, 12, 15, … is 48? (a) 16th (b) 17th (c) 15th (d) 14th
  38. 38.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 180 (b) 96 (c) 20 (d) 90
  39. 39.What is the 31st term of the AP 11, 17, 23, 29, …? (a) 180 (b) 191 (c) 197 (d) 186
  40. 40.What is the 32nd term of the AP 6, 12, 18, 24, …? (a) 193 (b) 186 (c) 192 (d) 198

Answer key

  1. 396
  2. 25
  3. 195
  4. 71
  5. 225
  6. 279
  7. 16
  8. 109
  9. 676
  10. 144
  11. 225
  12. 18
  13. 18th
  14. 56
  15. 4656
  16. 324
  17. 96
  18. 45
  19. 189
  20. 25
  21. 15th
  22. 99
  23. 25th
  24. 154
  25. 59
  26. 64
  27. 361
  28. 55
  29. 37
  30. 217
  31. 102
  32. 21st
  33. 340
  34. 144
  35. 12th
  36. 325
  37. 15th
  38. 90
  39. 191
  40. 192

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