← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 81 · 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.Which term of the AP 1, 8, 15, 22, … is 71? (a) 10th (b) 11th (c) 12th (d) 13th
  2. 2.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  3. 3.What is the 34th term of the AP 8, 14, 20, 26, …? (a) 204 (b) 198 (c) 212 (d) 206
  4. 4.What is the missing term in the AP 16, ?, 28, 34, 40? (a) 28 (b) 21 (c) 22 (d) 23
  5. 5.What is the 37th term of the AP 2, 6, 10, 14, …? (a) 148 (b) 150 (c) 144 (d) 146
  6. 6.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 112 (c) 216 (d) 108
  7. 7.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 2256 (c) 1081 (d) 1128
  8. 8.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 276 (d) 552
  9. 9.What is the 18th term of the AP 19, 27, 35, 43, …? (a) 144 (b) 155 (c) 163 (d) 136
  10. 10.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 5 (b) 6 (c) 3 (d) 4
  11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
  12. 12.What is the 35th term of the AP 3, 9, 15, 21, …? (a) 213 (b) 204 (c) 210 (d) 207
  13. 13.What is the 36th term of the AP 18, 20, 22, 24, …? (a) 90 (b) 70 (c) 88 (d) 72
  14. 14.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 256 (d) 31
  15. 15.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 231 (c) 462 (d) 232
  16. 16.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 35 (b) 26 (c) 28 (d) 27
  17. 17.What is the 22nd term of the AP 15, 17, 19, 21, …? (a) 42 (b) 59 (c) 57 (d) 44
  18. 18.Which term of the AP 2, 11, 20, 29, … is 128? (a) 16th (b) 15th (c) 14th (d) 17th
  19. 19.What is the missing term in the AP 8, 11, ?, 17, 20? (a) 13 (b) 17 (c) 15 (d) 14
  20. 20.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 340 (b) 370 (c) 680 (d) 61
  21. 21.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 44 (b) 46 (c) 45 (d) 54
  22. 22.What is the 26th term of the AP 11, 17, 23, 29, …? (a) 156 (b) 167 (c) 150 (d) 161
  23. 23.What is the 33rd term of the AP 5, 12, 19, 26, …? (a) 236 (b) 229 (c) 231 (d) 224
  24. 24.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 70 (b) 35 (c) 13 (d) 38
  25. 25.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 5 (b) 3 (c) 4 (d) 2
  26. 26.Which term of the AP 11, 16, 21, 26, … is 96? (a) 20th (b) 17th (c) 19th (d) 18th
  27. 27.What is the 15th term of the AP 19, 26, 33, 40, …? (a) 98 (b) 105 (c) 117 (d) 124
  28. 28.What is the 17th term of the AP 14, 16, 18, 20, …? (a) 48 (b) 32 (c) 34 (d) 46
  29. 29.What is the 21st term of the AP 20, 24, 28, 32, …? (a) 104 (b) 100 (c) 84 (d) 80
  30. 30.What is the 39th term of the AP 7, 11, 15, 19, …? (a) 163 (b) 156 (c) 152 (d) 159
  31. 31.What is the 15th term of the AP 13, 16, 19, 22, …? (a) 42 (b) 58 (c) 45 (d) 55
  32. 32.What is the 36th term of the AP 20, 24, 28, 32, …? (a) 140 (b) 160 (c) 144 (d) 164
  33. 33.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 600 (c) 276 (d) 288
  34. 34.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 120 (b) 21 (c) 112 (d) 224
  35. 35.What is the 18th term of the AP 5, 13, 21, 29, …? (a) 141 (b) 144 (c) 136 (d) 149
  36. 36.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 240 (b) 220 (c) 40 (d) 440
  37. 37.Which term of the AP 12, 19, 26, 33, … is 75? (a) 9th (b) 12th (c) 10th (d) 11th
  38. 38.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 6320 (c) 3161 (d) 3081
  39. 39.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 136 (c) 154 (d) 153
  40. 40.What is the 27th term of the AP 14, 17, 20, 23, …? (a) 95 (b) 81 (c) 92 (d) 78

Answer key

  1. 11th
  2. 25
  3. 206
  4. 22
  5. 146
  6. 108
  7. 1128
  8. 529
  9. 155
  10. 4
  11. 121
  12. 207
  13. 88
  14. 256
  15. 231
  16. 27
  17. 57
  18. 15th
  19. 14
  20. 340
  21. 45
  22. 161
  23. 229
  24. 35
  25. 3
  26. 18th
  27. 117
  28. 46
  29. 100
  30. 159
  31. 55
  32. 160
  33. 300
  34. 112
  35. 141
  36. 220
  37. 10th
  38. 3160
  39. 153
  40. 92

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