← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 66 · 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 39th term of the AP 6, 14, 22, 30, …? (a) 312 (b) 318 (c) 310 (d) 304
  2. 2.What is the 40th term of the AP 10, 14, 18, 22, …? (a) 170 (b) 156 (c) 160 (d) 166
  3. 3.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 344 (b) 39 (c) 192 (d) 172
  4. 4.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 117 (b) 20 (c) 216 (d) 108
  5. 5.What is the 17th term of the AP 8, 12, 16, 20, …? (a) 68 (b) 72 (c) 64 (d) 76
  6. 6.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 110 (d) 100
  7. 7.What is the 10th term of the AP 6, 14, 22, 30, …? (a) 86 (b) 72 (c) 78 (d) 80
  8. 8.What is the 18th term of the AP 4, 6, 8, 10, …? (a) 36 (b) 38 (c) 34 (d) 40
  9. 9.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 24 (b) 21 (c) 22 (d) 23
  10. 10.What is the 36th term of the AP 2, 4, 6, 8, …? (a) 72 (b) 73 (c) 74 (d) 70
  11. 11.Which term of the AP 15, 19, 23, 27, … is 79? (a) 16th (b) 18th (c) 19th (d) 17th
  12. 12.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 1953 (c) 4032 (d) 2017
  13. 13.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 43 (d) 484
  14. 14.What is the 26th term of the AP 13, 17, 21, 25, …? (a) 104 (b) 113 (c) 117 (d) 100
  15. 15.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 76 (b) 552 (c) 516 (d) 1032
  16. 16.What is the 22nd term of the AP 16, 23, 30, 37, …? (a) 147 (b) 163 (c) 154 (d) 170
  17. 17.What is the 12th term of the AP 16, 23, 30, 37, …? (a) 100 (b) 77 (c) 93 (d) 84
  18. 18.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 60 (b) 30 (c) 35 (d) 10
  19. 19.What is the 28th term of the AP 15, 17, 19, 21, …? (a) 56 (b) 69 (c) 54 (d) 71
  20. 20.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 9 (b) 8 (c) 6 (d) 7
  21. 21.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 234 (b) 21 (c) 117 (d) 126
  22. 22.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 182 (c) 78 (d) 92
  23. 23.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 272 (d) 136
  24. 24.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 192 (b) 108 (c) 26 (d) 96
  25. 25.Which term of the AP 20, 26, 32, 38, … is 116? (a) 18th (b) 19th (c) 16th (d) 17th
  26. 26.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 12 (b) 80 (c) 40 (d) 45
  27. 27.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 20 (b) 73 (c) 140 (d) 70
  28. 28.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 190 (d) 361
  29. 29.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 64 (b) 126 (c) 63 (d) 11
  30. 30.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 105 (c) 27 (d) 210
  31. 31.What is the 34th term of the AP 13, 20, 27, 34, …? (a) 231 (b) 238 (c) 251 (d) 244
  32. 32.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 420 (d) 39
  33. 33.What is the 27th term of the AP 5, 14, 23, 32, …? (a) 239 (b) 243 (c) 248 (d) 234
  34. 34.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 1056 (c) 528 (d) 496
  35. 35.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 18 (b) 21 (c) 17 (d) 16
  36. 36.What is the 10th term of the AP 3, 12, 21, 30, …? (a) 90 (b) 81 (c) 93 (d) 84
  37. 37.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 105 (c) 210 (d) 114
  38. 38.Which term of the AP 17, 24, 31, 38, … is 269? (a) 36th (b) 38th (c) 39th (d) 37th
  39. 39.What is the 11th term of the AP 9, 14, 19, 24, …? (a) 64 (b) 50 (c) 59 (d) 55
  40. 40.What is the 34th term of the AP 10, 18, 26, 34, …? (a) 272 (b) 274 (c) 264 (d) 282

Answer key

  1. 310
  2. 166
  3. 172
  4. 108
  5. 72
  6. 100
  7. 78
  8. 38
  9. 22
  10. 72
  11. 17th
  12. 2016
  13. 484
  14. 113
  15. 516
  16. 163
  17. 93
  18. 30
  19. 69
  20. 7
  21. 117
  22. 91
  23. 256
  24. 96
  25. 17th
  26. 40
  27. 70
  28. 361
  29. 63
  30. 196
  31. 244
  32. 400
  33. 239
  34. 528
  35. 17
  36. 84
  37. 105
  38. 37th
  39. 59
  40. 274

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