← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 644 · 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 10, 16, 22, …? (a) 70 (b) 440 (c) 473 (d) 880
  2. 2.What is the 33rd term of the AP 18, 22, 26, 30, …? (a) 150 (b) 146 (c) 132 (d) 128
  3. 3.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  4. 4.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 180 (b) 95 (c) 28 (d) 90
  5. 5.Which term of the AP 14, 22, 30, 38, … is 246? (a) 32nd (b) 30th (c) 29th (d) 31st
  6. 6.Which term of the AP 7, 10, 13, 16, … is 103? (a) 34th (b) 35th (c) 32nd (d) 33rd
  7. 7.What is the 11th term of the AP 6, 10, 14, 18, …? (a) 44 (b) 40 (c) 50 (d) 46
  8. 8.What is the 32nd term of the AP 8, 12, 16, 20, …? (a) 136 (b) 128 (c) 124 (d) 132
  9. 9.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 11 (b) 21 (c) 13 (d) 12
  10. 10.What is the 30th term of the AP 3, 6, 9, 12, …? (a) 90 (b) 87 (c) 91 (d) 93
  11. 11.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 946 (c) 1892 (d) 947
  12. 12.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 12 (b) 11 (c) 13 (d) 19
  13. 13.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 78 (b) 156 (c) 84 (d) 18
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72
  15. 15.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 34 (b) 144 (c) 129 (d) 258
  16. 16.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 12 (b) 10 (c) 11 (d) 13
  17. 17.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 243 (b) 486 (c) 47 (d) 248
  18. 18.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 192 (b) 21 (c) 372 (d) 186
  19. 19.What is the 25th term of the AP 13, 16, 19, 22, …? (a) 72 (b) 75 (c) 88 (d) 85
  20. 20.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 248 (b) 448 (c) 49 (d) 224
  21. 21.Which term of the AP 4, 6, 8, 10, … is 50? (a) 23rd (b) 25th (c) 26th (d) 24th
  22. 22.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 2070 (c) 1036 (d) 1035
  23. 23.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 150 (b) 84 (c) 75 (d) 20
  24. 24.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 572 (b) 286 (c) 51 (d) 291
  25. 25.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 147 (c) 31 (d) 133
  26. 26.What is the 11th term of the AP 4, 12, 20, 28, …? (a) 92 (b) 88 (c) 84 (d) 80
  27. 27.What is the 19th term of the AP 18, 24, 30, 36, …? (a) 114 (b) 132 (c) 126 (d) 108
  28. 28.What is the missing term in the AP 9, 16, 23, ?, 37? (a) 30 (b) 31 (c) 29 (d) 37
  29. 29.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 34 (b) 27 (c) 28 (d) 26
  30. 30.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 80 (b) 65 (c) 130 (d) 25
  31. 31.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 91 (d) 182
  32. 32.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 484 (d) 43
  33. 33.What is the 19th term of the AP 7, 13, 19, 25, …? (a) 115 (b) 121 (c) 114 (d) 108
  34. 34.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 27 (b) 33 (c) 26 (d) 25
  35. 35.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 4187 (c) 8372 (d) 4186
  36. 36.What is the 14th term of the AP 20, 23, 26, 29, …? (a) 42 (b) 62 (c) 39 (d) 59
  37. 37.What is the 20th term of the AP 1, 5, 9, 13, …? (a) 81 (b) 77 (c) 76 (d) 80
  38. 38.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 234 (b) 216 (c) 40 (d) 432
  39. 39.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 22 (b) 140 (c) 260 (d) 130
  40. 40.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 496 (d) 992

Answer key

  1. 440
  2. 146
  3. 729
  4. 90
  5. 30th
  6. 33rd
  7. 46
  8. 132
  9. 12
  10. 90
  11. 946
  12. 12
  13. 78
  14. 64
  15. 129
  16. 11
  17. 243
  18. 186
  19. 85
  20. 224
  21. 24th
  22. 1035
  23. 75
  24. 286
  25. 133
  26. 84
  27. 126
  28. 30
  29. 27
  30. 65
  31. 169
  32. 484
  33. 115
  34. 26
  35. 4186
  36. 59
  37. 77
  38. 216
  39. 130
  40. 496

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