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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 699 · 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 12, 17, 22, 27, … is 157? (a) 29th (b) 31st (c) 32nd (d) 30th
  2. 2.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 19 (b) 162 (c) 168 (d) 324
  3. 3.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 212 (b) 34 (c) 209 (d) 418
  4. 4.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 374 (b) 27 (c) 198 (d) 187
  5. 5.Which term of the AP 1, 4, 7, 10, … is 106? (a) 38th (b) 35th (c) 37th (d) 36th
  6. 6.What is the 23rd term of the AP 5, 14, 23, 32, …? (a) 207 (b) 203 (c) 198 (d) 212
  7. 7.Which term of the AP 11, 15, 19, 23, … is 79? (a) 19th (b) 20th (c) 17th (d) 18th
  8. 8.Which term of the AP 12, 18, 24, 30, … is 156? (a) 26th (b) 24th (c) 27th (d) 25th
  9. 9.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 650 (b) 350 (c) 325 (d) 55
  10. 10.Which term of the AP 15, 23, 31, 39, … is 87? (a) 12th (b) 9th (c) 10th (d) 11th
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  12. 12.What is the 16th term of the AP 5, 13, 21, 29, …? (a) 125 (b) 133 (c) 120 (d) 128
  13. 13.What is the 16th term of the AP 5, 8, 11, 14, …? (a) 50 (b) 48 (c) 53 (d) 45
  14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
  15. 15.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 85 (b) 29 (c) 100 (d) 170
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
  17. 17.Which term of the AP 18, 23, 28, 33, … is 183? (a) 35th (b) 36th (c) 33rd (d) 34th
  18. 18.What is the 28th term of the AP 3, 10, 17, 24, …? (a) 192 (b) 199 (c) 189 (d) 196
  19. 19.What is the 17th term of the AP 4, 7, 10, 13, …? (a) 48 (b) 55 (c) 51 (d) 52
  20. 20.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 154 (c) 153 (d) 136
  21. 21.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 162 (b) 30 (c) 324 (d) 165
  22. 22.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 992 (d) 496
  23. 23.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 40 (b) 41 (c) 50 (d) 42
  24. 24.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 2346 (c) 2278 (d) 4692
  25. 25.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 140 (b) 70 (c) 71 (d) 13
  26. 26.Which term of the AP 18, 23, 28, 33, … is 123? (a) 23rd (b) 22nd (c) 21st (d) 24th
  27. 27.Which term of the AP 16, 25, 34, 43, … is 205? (a) 24th (b) 23rd (c) 21st (d) 22nd
  28. 28.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 20 (b) 22 (c) 23 (d) 21
  29. 29.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 60 (b) 50 (c) 18 (d) 100
  30. 30.What is the 21st term of the AP 2, 7, 12, 17, …? (a) 100 (b) 102 (c) 105 (d) 107
  31. 31.What is the 39th term of the AP 7, 14, 21, 28, …? (a) 274 (b) 266 (c) 273 (d) 280
  32. 32.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 460 (b) 250 (c) 230 (d) 41
  33. 33.Which term of the AP 6, 13, 20, 27, … is 104? (a) 16th (b) 17th (c) 15th (d) 14th
  34. 34.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 144 (b) 72 (c) 78 (d) 17
  35. 35.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 176 (b) 31 (c) 352 (d) 179
  36. 36.What is the 27th term of the AP 19, 22, 25, 28, …? (a) 78 (b) 81 (c) 100 (d) 97
  37. 37.Which term of the AP 1, 4, 7, 10, … is 64? (a) 22nd (b) 23rd (c) 21st (d) 24th
  38. 38.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 1560 (c) 780 (d) 741
  39. 39.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 182 (d) 91
  40. 40.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 72 (d) 36

Answer key

  1. 30th
  2. 162
  3. 209
  4. 187
  5. 36th
  6. 203
  7. 18th
  8. 25th
  9. 325
  10. 10th
  11. 144
  12. 125
  13. 50
  14. 729
  15. 85
  16. 121
  17. 34th
  18. 192
  19. 52
  20. 153
  21. 162
  22. 496
  23. 41
  24. 2346
  25. 70
  26. 22nd
  27. 22nd
  28. 21
  29. 50
  30. 102
  31. 273
  32. 230
  33. 15th
  34. 72
  35. 176
  36. 97
  37. 22nd
  38. 780
  39. 169
  40. 64

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