← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 322 · 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 2, 8, 14, …? (a) 32 (b) 120 (c) 204 (d) 102
  2. 2.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 63 (b) 15 (c) 126 (d) 70
  3. 3.What is the 27th term of the AP 3, 12, 21, 30, …? (a) 243 (b) 246 (c) 237 (d) 234
  4. 4.What is the sum of all the whole numbers from 1 to 68? (a) 2346 (b) 2312 (c) 2278 (d) 4692
  5. 5.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 506 (d) 43
  6. 6.Which term of the AP 9, 14, 19, 24, … is 99? (a) 19th (b) 20th (c) 21st (d) 18th
  7. 7.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 4050 (c) 8190 (d) 4095
  8. 8.Which term of the AP 20, 22, 24, 26, … is 58? (a) 21st (b) 20th (c) 19th (d) 29th
  9. 9.Which term of the AP 8, 12, 16, 20, … is 88? (a) 22nd (b) 23rd (c) 20th (d) 21st
  10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 196 (d) 105
  11. 11.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 96 (b) 84 (c) 168 (d) 24
  12. 12.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 123 (b) 33 (c) 138 (d) 246
  13. 13.What is the 21st term of the AP 20, 23, 26, 29, …? (a) 83 (b) 63 (c) 60 (d) 80
  14. 14.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 2016 (c) 4032 (d) 1953
  15. 15.What is the 36th term of the AP 2, 9, 16, 23, …? (a) 254 (b) 247 (c) 245 (d) 252
  16. 16.What is the 24th term of the AP 13, 16, 19, 22, …? (a) 72 (b) 69 (c) 85 (d) 82
  17. 17.What is the 40th term of the AP 7, 16, 25, 34, …? (a) 351 (b) 360 (c) 358 (d) 367
  18. 18.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 98 (b) 112 (c) 196 (d) 26
  19. 19.What is the 22nd term of the AP 6, 8, 10, 12, …? (a) 48 (b) 42 (c) 44 (d) 50
  20. 20.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 702 (d) 351
  21. 21.What is the 19th term of the AP 14, 23, 32, 41, …? (a) 185 (b) 162 (c) 171 (d) 176
  22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
  23. 23.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 13 (b) 20 (c) 11 (d) 12
  24. 24.What is the 24th term of the AP 3, 11, 19, 27, …? (a) 195 (b) 192 (c) 184 (d) 187
  25. 25.What is the 40th term of the AP 3, 11, 19, 27, …? (a) 320 (b) 323 (c) 315 (d) 312
  26. 26.What is the 33rd term of the AP 3, 5, 7, 9, …? (a) 69 (b) 64 (c) 66 (d) 67
  27. 27.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 4095 (c) 8372 (d) 4187
  28. 28.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 406 (c) 435 (d) 870
  29. 29.What is the 28th term of the AP 4, 8, 12, 16, …? (a) 108 (b) 112 (c) 113 (d) 116
  30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 35 (d) 342
  31. 31.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 21 (b) 18 (c) 19 (d) 20
  32. 32.What is the 20th term of the AP 6, 10, 14, 18, …? (a) 80 (b) 76 (c) 86 (d) 82
  33. 33.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 15 (b) 16 (c) 18 (d) 14
  34. 34.What is the missing term in the AP 13, 16, ?, 22, 25? (a) 18 (b) 20 (c) 19 (d) 22
  35. 35.Which term of the AP 11, 18, 25, 32, … is 256? (a) 38th (b) 36th (c) 37th (d) 35th
  36. 36.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 90 (b) 80 (c) 160 (d) 24
  37. 37.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 29 (b) 39 (c) 31 (d) 30
  38. 38.Which term of the AP 10, 13, 16, 19, … is 112? (a) 36th (b) 37th (c) 34th (d) 35th
  39. 39.What is the missing term in the AP 15, 17, ?, 21, 23? (a) 19 (b) 21 (c) 20 (d) 18
  40. 40.What is the 31st term of the AP 17, 19, 21, 23, …? (a) 62 (b) 79 (c) 77 (d) 60

Answer key

  1. 102
  2. 63
  3. 237
  4. 2346
  5. 484
  6. 19th
  7. 4095
  8. 20th
  9. 21st
  10. 196
  11. 84
  12. 123
  13. 80
  14. 2016
  15. 247
  16. 82
  17. 358
  18. 98
  19. 48
  20. 676
  21. 176
  22. 121
  23. 12
  24. 187
  25. 315
  26. 67
  27. 4186
  28. 435
  29. 112
  30. 324
  31. 19
  32. 82
  33. 15
  34. 19
  35. 36th
  36. 80
  37. 30
  38. 35th
  39. 19
  40. 77

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