← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 793 · 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 all the whole numbers from 1 to 86? (a) 3698 (b) 3655 (c) 7482 (d) 3741
  2. 2.What is the 27th term of the AP 2, 5, 8, 11, …? (a) 81 (b) 78 (c) 80 (d) 83
  3. 3.What is the 12th term of the AP 3, 5, 7, 9, …? (a) 25 (b) 22 (c) 24 (d) 27
  4. 4.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 17 (b) 10 (c) 8 (d) 9
  5. 5.What is the 24th term of the AP 17, 19, 21, 23, …? (a) 46 (b) 48 (c) 63 (d) 65
  6. 6.What is the 11th term of the AP 15, 21, 27, 33, …? (a) 75 (b) 81 (c) 60 (d) 66
  7. 7.Which term of the AP 8, 11, 14, 17, … is 116? (a) 38th (b) 37th (c) 39th (d) 36th
  8. 8.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 4278 (c) 8742 (d) 4372
  9. 9.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1540 (c) 1485 (d) 3080
  10. 10.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1653 (c) 1654 (d) 3306
  11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 210 (d) 105
  12. 12.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 336 (b) 48 (c) 312 (d) 624
  13. 13.What is the 33rd term of the AP 7, 10, 13, 16, …? (a) 106 (b) 96 (c) 99 (d) 103
  14. 14.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 31 (c) 240 (d) 480
  15. 15.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 72 (b) 138 (c) 14 (d) 69
  16. 16.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 325 (d) 49
  17. 17.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 50 (c) 55 (d) 45
  18. 18.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 280 (b) 255 (c) 48 (d) 510
  19. 19.What is the 15th term of the AP 14, 17, 20, 23, …? (a) 42 (b) 56 (c) 45 (d) 59
  20. 20.Which term of the AP 17, 19, 21, 23, … is 31? (a) 7th (b) 10th (c) 8th (d) 9th
  21. 21.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 25 (b) 20 (c) 19 (d) 18
  22. 22.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 15 (b) 16 (c) 20 (d) 17
  23. 23.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 70 (d) 35
  24. 24.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 9 (b) 7 (c) 8 (d) 12
  25. 25.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 32 (b) 140 (c) 280 (d) 154
  26. 26.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 31 (b) 179 (c) 352 (d) 176
  27. 27.What is the 17th term of the AP 9, 12, 15, 18, …? (a) 60 (b) 57 (c) 48 (d) 51
  28. 28.What is the 26th term of the AP 9, 14, 19, 24, …? (a) 134 (b) 139 (c) 125 (d) 130
  29. 29.Which term of the AP 3, 12, 21, 30, … is 318? (a) 35th (b) 36th (c) 37th (d) 38th
  30. 30.What is the 16th term of the AP 18, 20, 22, 24, …? (a) 30 (b) 50 (c) 32 (d) 48
  31. 31.What is the 28th term of the AP 13, 15, 17, 19, …? (a) 67 (b) 56 (c) 69 (d) 54
  32. 32.What is the missing term in the AP 11, 14, ?, 20, 23? (a) 16 (b) 20 (c) 17 (d) 18
  33. 33.What is the 33rd term of the AP 19, 22, 25, 28, …? (a) 118 (b) 96 (c) 115 (d) 99
  34. 34.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 6642 (c) 3321 (d) 3240
  35. 35.What is the 29th term of the AP 16, 23, 30, 37, …? (a) 203 (b) 212 (c) 196 (d) 219
  36. 36.What is the 37th term of the AP 14, 19, 24, 29, …? (a) 180 (b) 199 (c) 185 (d) 194
  37. 37.What is the 14th term of the AP 4, 9, 14, 19, …? (a) 74 (b) 70 (c) 69 (d) 65
  38. 38.Which term of the AP 19, 21, 23, 25, … is 67? (a) 26th (b) 24th (c) 27th (d) 25th
  39. 39.What is the 30th term of the AP 12, 14, 16, 18, …? (a) 72 (b) 58 (c) 60 (d) 70
  40. 40.What is the 32nd term of the AP 17, 25, 33, 41, …? (a) 256 (b) 248 (c) 273 (d) 265

Answer key

  1. 3741
  2. 80
  3. 25
  4. 9
  5. 63
  6. 75
  7. 37th
  8. 4371
  9. 1540
  10. 1653
  11. 196
  12. 312
  13. 103
  14. 240
  15. 69
  16. 625
  17. 55
  18. 255
  19. 56
  20. 8th
  21. 19
  22. 16
  23. 35
  24. 8
  25. 140
  26. 176
  27. 57
  28. 134
  29. 36th
  30. 48
  31. 67
  32. 17
  33. 115
  34. 3321
  35. 212
  36. 194
  37. 69
  38. 25th
  39. 70
  40. 265

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