← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 623 · 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 7 terms of the AP 10, 16, 22, …? (a) 392 (b) 217 (c) 46 (d) 196
  2. 2.Which term of the AP 18, 27, 36, 45, … is 270? (a) 29th (b) 30th (c) 31st (d) 28th
  3. 3.What is the 26th term of the AP 17, 23, 29, 35, …? (a) 173 (b) 150 (c) 156 (d) 167
  4. 4.Which term of the AP 8, 14, 20, 26, … is 170? (a) 27th (b) 28th (c) 30th (d) 29th
  5. 5.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 19 (b) 20 (c) 21 (d) 18
  6. 6.What is the 17th term of the AP 6, 12, 18, 24, …? (a) 108 (b) 103 (c) 102 (d) 96
  7. 7.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  8. 8.What is the 10th term of the AP 17, 22, 27, 32, …? (a) 50 (b) 62 (c) 67 (d) 45
  9. 9.What is the 29th term of the AP 12, 14, 16, 18, …? (a) 68 (b) 70 (c) 56 (d) 58
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 256 (d) 272
  11. 11.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 25 (b) 26 (c) 24 (d) 23
  12. 12.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 2256 (c) 1129 (d) 1081
  13. 13.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576
  14. 14.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3528 (c) 3570 (d) 7140
  15. 15.What is the 18th term of the AP 14, 22, 30, 38, …? (a) 136 (b) 144 (c) 150 (d) 158
  16. 16.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 180 (b) 36 (c) 198 (d) 360
  17. 17.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 65 (b) 385 (c) 418 (d) 770
  18. 18.What is the 16th term of the AP 7, 14, 21, 28, …? (a) 113 (b) 112 (c) 105 (d) 119
  19. 19.What is the 19th term of the AP 12, 20, 28, 36, …? (a) 152 (b) 144 (c) 156 (d) 164
  20. 20.Which term of the AP 5, 14, 23, 32, … is 203? (a) 23rd (b) 24th (c) 25th (d) 22nd
  21. 21.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 14 (b) 22 (c) 15 (d) 13
  22. 22.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 184 (b) 336 (c) 35 (d) 168
  23. 23.Which term of the AP 15, 23, 31, 39, … is 303? (a) 38th (b) 36th (c) 39th (d) 37th
  24. 24.What is the 39th term of the AP 16, 18, 20, 22, …? (a) 78 (b) 92 (c) 94 (d) 76
  25. 25.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 114 (b) 132 (c) 34 (d) 228
  26. 26.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 2628 (c) 5402 (d) 2701
  27. 27.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 117 (c) 118 (d) 17
  28. 28.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 140 (b) 270 (c) 135 (d) 18
  29. 29.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 90 (b) 48 (c) 45 (d) 10
  30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 66 (d) 21
  31. 31.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 12 (b) 11 (c) 16 (d) 10
  32. 32.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 120 (b) 24 (c) 108 (d) 216
  33. 33.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 120 (c) 272 (d) 136
  34. 34.What is the 12th term of the AP 20, 22, 24, 26, …? (a) 22 (b) 24 (c) 44 (d) 42
  35. 35.What is the 11th term of the AP 6, 12, 18, 24, …? (a) 66 (b) 72 (c) 67 (d) 60
  36. 36.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 129 (b) 34 (c) 144 (d) 258
  37. 37.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 8930 (c) 4465 (d) 4418
  38. 38.What is the 15th term of the AP 3, 10, 17, 24, …? (a) 98 (b) 108 (c) 101 (d) 105
  39. 39.What is the 38th term of the AP 2, 6, 10, 14, …? (a) 152 (b) 150 (c) 154 (d) 148
  40. 40.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276

Answer key

  1. 196
  2. 29th
  3. 167
  4. 28th
  5. 19
  6. 102
  7. 144
  8. 62
  9. 68
  10. 256
  11. 24
  12. 1128
  13. 576
  14. 3570
  15. 150
  16. 180
  17. 385
  18. 112
  19. 156
  20. 23rd
  21. 14
  22. 168
  23. 37th
  24. 92
  25. 114
  26. 2701
  27. 117
  28. 135
  29. 45
  30. 121
  31. 11
  32. 108
  33. 136
  34. 42
  35. 66
  36. 129
  37. 4465
  38. 101
  39. 150
  40. 529

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