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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 700 · 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 33rd term of the AP 6, 10, 14, 18, …? (a) 138 (b) 132 (c) 128 (d) 134
  2. 2.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1953 (c) 1922 (d) 1891
  3. 3.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 15 (b) 14 (c) 13 (d) 12
  4. 4.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 888 (b) 480 (c) 70 (d) 444
  5. 5.What is the 35th term of the AP 6, 13, 20, 27, …? (a) 244 (b) 238 (c) 245 (d) 251
  6. 6.Which term of the AP 2, 6, 10, 14, … is 38? (a) 9th (b) 10th (c) 12th (d) 11th
  7. 7.Which term of the AP 4, 12, 20, 28, … is 108? (a) 14th (b) 16th (c) 15th (d) 13th
  8. 8.What is the 18th term of the AP 15, 23, 31, 39, …? (a) 136 (b) 144 (c) 151 (d) 159
  9. 9.What is the 32nd term of the AP 2, 10, 18, 26, …? (a) 256 (b) 248 (c) 250 (d) 258
  10. 10.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 18 (b) 17 (c) 21 (d) 19
  11. 11.What is the 24th term of the AP 2, 11, 20, 29, …? (a) 218 (b) 207 (c) 209 (d) 216
  12. 12.What is the 11th term of the AP 8, 12, 16, 20, …? (a) 48 (b) 44 (c) 52 (d) 40
  13. 13.What is the 39th term of the AP 7, 13, 19, 25, …? (a) 234 (b) 235 (c) 241 (d) 228
  14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 59 (c) 930 (d) 465
  15. 15.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3003 (c) 6162 (d) 3081
  16. 16.What is the 21st term of the AP 18, 26, 34, 42, …? (a) 178 (b) 186 (c) 168 (d) 160
  17. 17.Which term of the AP 13, 20, 27, 34, … is 216? (a) 29th (b) 32nd (c) 31st (d) 30th
  18. 18.What is the 27th term of the AP 19, 28, 37, 46, …? (a) 253 (b) 243 (c) 234 (d) 262
  19. 19.Which term of the AP 16, 21, 26, 31, … is 66? (a) 10th (b) 13th (c) 11th (d) 12th
  20. 20.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 19 (b) 69 (c) 138 (d) 78
  21. 21.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 210 (b) 25 (c) 114 (d) 105
  22. 22.What is the 35th term of the AP 15, 19, 23, 27, …? (a) 151 (b) 136 (c) 140 (d) 155
  23. 23.Which term of the AP 19, 26, 33, 40, … is 152? (a) 20th (b) 22nd (c) 21st (d) 19th
  24. 24.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3528 (c) 3486 (d) 3570
  25. 25.What is the 29th term of the AP 16, 20, 24, 28, …? (a) 116 (b) 132 (c) 112 (d) 128
  26. 26.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 37 (d) 190
  27. 27.What is the 21st term of the AP 11, 13, 15, 17, …? (a) 53 (b) 42 (c) 40 (d) 51
  28. 28.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1653 (c) 1711 (d) 1682
  29. 29.What is the 28th term of the AP 10, 13, 16, 19, …? (a) 91 (b) 94 (c) 81 (d) 84
  30. 30.What is the 29th term of the AP 7, 12, 17, 22, …? (a) 145 (b) 140 (c) 152 (d) 147
  31. 31.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 24 (b) 20 (c) 19 (d) 21
  32. 32.Which term of the AP 7, 15, 23, 31, … is 175? (a) 23rd (b) 24th (c) 21st (d) 22nd
  33. 33.What is the 34th term of the AP 5, 8, 11, 14, …? (a) 107 (b) 99 (c) 104 (d) 102
  34. 34.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 54 (b) 384 (c) 768 (d) 408
  35. 35.What is the 21st term of the AP 8, 16, 24, 32, …? (a) 169 (b) 160 (c) 168 (d) 176
  36. 36.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 76 (b) 1032 (c) 552 (d) 516
  37. 37.Which term of the AP 16, 19, 22, 25, … is 49? (a) 13th (b) 12th (c) 11th (d) 14th
  38. 38.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 46 (b) 239 (c) 468 (d) 234
  39. 39.What is the 31st term of the AP 19, 23, 27, 31, …? (a) 120 (b) 143 (c) 139 (d) 124
  40. 40.Which term of the AP 19, 21, 23, 25, … is 73? (a) 29th (b) 28th (c) 30th (d) 27th

Answer key

  1. 134
  2. 1953
  3. 13
  4. 444
  5. 244
  6. 10th
  7. 14th
  8. 151
  9. 250
  10. 18
  11. 209
  12. 48
  13. 235
  14. 900
  15. 3081
  16. 178
  17. 30th
  18. 253
  19. 11th
  20. 69
  21. 105
  22. 151
  23. 20th
  24. 3570
  25. 128
  26. 361
  27. 51
  28. 1711
  29. 91
  30. 147
  31. 20
  32. 22nd
  33. 104
  34. 384
  35. 168
  36. 516
  37. 12th
  38. 234
  39. 139
  40. 28th

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