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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 589 · 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 6 terms of the AP 8, 10, 12, …? (a) 84 (b) 78 (c) 156 (d) 18
  2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 78 (d) 156
  3. 3.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 252 (b) 140 (c) 30 (d) 126
  4. 4.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 52 (b) 360 (c) 720 (d) 384
  5. 5.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 29 (b) 25 (c) 26 (d) 27
  6. 6.What is the 18th term of the AP 6, 10, 14, 18, …? (a) 72 (b) 68 (c) 74 (d) 78
  7. 7.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 28 (b) 160 (c) 80 (d) 95
  8. 8.What is the 13th term of the AP 8, 16, 24, 32, …? (a) 96 (b) 112 (c) 105 (d) 104
  9. 9.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 18 (b) 286 (c) 144 (d) 143
  10. 10.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 21 (b) 19 (c) 28 (d) 20
  11. 11.What is the 16th term of the AP 7, 16, 25, 34, …? (a) 144 (b) 135 (c) 142 (d) 151
  12. 12.What is the 37th term of the AP 15, 22, 29, 36, …? (a) 274 (b) 259 (c) 252 (d) 267
  13. 13.What is the 19th term of the AP 13, 22, 31, 40, …? (a) 171 (b) 175 (c) 184 (d) 162
  14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  15. 15.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 1176 (c) 1225 (d) 2450
  16. 16.Which term of the AP 19, 26, 33, 40, … is 96? (a) 11th (b) 12th (c) 14th (d) 13th
  17. 17.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 253 (c) 231 (d) 506
  18. 18.Which term of the AP 5, 12, 19, 26, … is 61? (a) 9th (b) 10th (c) 11th (d) 8th
  19. 19.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 225 (b) 36 (c) 240 (d) 450
  20. 20.What is the 29th term of the AP 6, 15, 24, 33, …? (a) 267 (b) 261 (c) 258 (d) 252
  21. 21.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 138 (c) 240 (d) 120
  22. 22.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 216 (b) 120 (c) 24 (d) 108
  23. 23.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  24. 24.What is the 19th term of the AP 18, 22, 26, 30, …? (a) 90 (b) 76 (c) 94 (d) 72
  25. 25.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 29 (b) 155 (c) 170 (d) 310
  26. 26.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 53 (b) 308 (c) 616 (d) 313
  27. 27.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 378 (d) 756
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  29. 29.What is the 33rd term of the AP 14, 17, 20, 23, …? (a) 96 (b) 110 (c) 99 (d) 113
  30. 30.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 29 (b) 56 (c) 7 (d) 28
  31. 31.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1711 (c) 1770 (d) 1771
  32. 32.What is the 16th term of the AP 6, 8, 10, 12, …? (a) 38 (b) 36 (c) 30 (d) 32
  33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 49 (d) 625
  34. 34.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 140 (b) 22 (c) 70 (d) 80
  35. 35.What is the 28th term of the AP 4, 12, 20, 28, …? (a) 220 (b) 224 (c) 216 (d) 228
  36. 36.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 198 (b) 29 (c) 114 (d) 99
  37. 37.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 136 (c) 153 (d) 154
  38. 38.What is the 15th term of the AP 15, 17, 19, 21, …? (a) 30 (b) 28 (c) 45 (d) 43
  39. 39.What is the 35th term of the AP 6, 10, 14, 18, …? (a) 136 (b) 140 (c) 146 (d) 142
  40. 40.Which term of the AP 5, 11, 17, 23, … is 113? (a) 18th (b) 21st (c) 20th (d) 19th

Answer key

  1. 78
  2. 144
  3. 126
  4. 360
  5. 26
  6. 74
  7. 80
  8. 104
  9. 143
  10. 20
  11. 142
  12. 267
  13. 175
  14. 289
  15. 1225
  16. 12th
  17. 253
  18. 9th
  19. 225
  20. 258
  21. 120
  22. 108
  23. 324
  24. 90
  25. 155
  26. 308
  27. 729
  28. 49
  29. 110
  30. 28
  31. 1770
  32. 36
  33. 625
  34. 70
  35. 220
  36. 99
  37. 153
  38. 43
  39. 142
  40. 19th

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