← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 562 · 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 17th term of the AP 12, 14, 16, 18, …? (a) 32 (b) 34 (c) 44 (d) 46
  2. 2.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 462 (d) 231
  3. 3.What is the missing term in the AP 2, ?, 20, 29, 38? (a) 11 (b) 20 (c) 10 (d) 12
  4. 4.Which term of the AP 5, 7, 9, 11, … is 63? (a) 31st (b) 29th (c) 32nd (d) 30th
  5. 5.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 55 (c) 67 (d) 132
  6. 6.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 14 (b) 11 (c) 12 (d) 10
  7. 7.What is the 32nd term of the AP 19, 21, 23, 25, …? (a) 64 (b) 81 (c) 83 (d) 62
  8. 8.What is the missing term in the AP 15, 22, ?, 36, 43? (a) 30 (b) 28 (c) 36 (d) 29
  9. 9.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 14 (b) 20 (c) 15 (d) 13
  10. 10.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 28 (b) 29 (c) 30 (d) 38
  11. 11.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 264 (b) 17 (c) 133 (d) 132
  12. 12.What is the 19th term of the AP 5, 12, 19, 26, …? (a) 133 (b) 126 (c) 131 (d) 138
  13. 13.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 120 (b) 234 (c) 117 (d) 25
  14. 14.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 25 (b) 21 (c) 20 (d) 22
  15. 15.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 4950 (c) 10100 (d) 5050
  16. 16.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 32 (b) 154 (c) 140 (d) 280
  17. 17.Which term of the AP 8, 11, 14, 17, … is 107? (a) 34th (b) 35th (c) 36th (d) 33rd
  18. 18.What is the missing term in the AP 20, 29, ?, 47, 56? (a) 47 (b) 38 (c) 39 (d) 37
  19. 19.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 51 (b) 240 (c) 264 (d) 480
  20. 20.What is the 31st term of the AP 5, 11, 17, 23, …? (a) 186 (b) 180 (c) 191 (d) 185
  21. 21.What is the 35th term of the AP 6, 14, 22, 30, …? (a) 280 (b) 286 (c) 278 (d) 272
  22. 22.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 19 (b) 17 (c) 18 (d) 22
  23. 23.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 72 (c) 66 (d) 78
  24. 24.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1128 (c) 1129 (d) 2256
  25. 25.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 225 (b) 450 (c) 45 (d) 230
  26. 26.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 18 (b) 70 (c) 75 (d) 140
  27. 27.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 20 (b) 23 (c) 21 (d) 22
  28. 28.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 338 (c) 702 (d) 325
  29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 484 (d) 253
  30. 30.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 4278 (c) 4371 (d) 8742
  31. 31.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 200 (b) 380 (c) 28 (d) 190
  32. 32.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 30 (d) 25
  33. 33.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 65 (b) 23 (c) 130 (d) 70
  34. 34.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 160 (b) 95 (c) 28 (d) 80
  35. 35.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 15 (b) 19 (c) 16 (d) 14
  36. 36.What is the missing term in the AP 12, 21, ?, 39, 48? (a) 31 (b) 29 (c) 30 (d) 39
  37. 37.What is the 13th term of the AP 15, 18, 21, 24, …? (a) 54 (b) 39 (c) 51 (d) 36
  38. 38.What is the 31st term of the AP 6, 12, 18, 24, …? (a) 186 (b) 187 (c) 192 (d) 180
  39. 39.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 6480 (c) 3200 (d) 3160
  40. 40.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 50 (c) 55 (d) 45

Answer key

  1. 44
  2. 441
  3. 11
  4. 30th
  5. 66
  6. 11
  7. 81
  8. 29
  9. 14
  10. 29
  11. 132
  12. 131
  13. 117
  14. 21
  15. 5050
  16. 140
  17. 34th
  18. 38
  19. 240
  20. 185
  21. 278
  22. 18
  23. 78
  24. 1128
  25. 225
  26. 70
  27. 21
  28. 351
  29. 484
  30. 4371
  31. 190
  32. 25
  33. 65
  34. 80
  35. 15
  36. 30
  37. 51
  38. 186
  39. 3240
  40. 55

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