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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 209 · 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 17th term of the AP 6, 11, 16, 21, …? (a) 91 (b) 85 (c) 80 (d) 86
  2. 2.What is the 23rd term of the AP 7, 16, 25, 34, …? (a) 214 (b) 205 (c) 198 (d) 207
  3. 3.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 16 (b) 22 (c) 14 (d) 15
  4. 4.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 1122 (c) 528 (d) 562
  5. 5.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 49 (d) 650
  6. 6.Which term of the AP 20, 23, 26, 29, … is 101? (a) 29th (b) 30th (c) 27th (d) 28th
  7. 7.What is the 16th term of the AP 6, 10, 14, 18, …? (a) 70 (b) 60 (c) 66 (d) 64
  8. 8.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 336 (b) 184 (c) 168 (d) 35
  9. 9.Which term of the AP 4, 9, 14, 19, … is 84? (a) 17th (b) 16th (c) 19th (d) 18th
  10. 10.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 55 (d) 784
  11. 11.What is the 16th term of the AP 7, 9, 11, 13, …? (a) 30 (b) 32 (c) 39 (d) 37
  12. 12.What is the missing term in the AP 19, 24, ?, 34, 39? (a) 30 (b) 34 (c) 29 (d) 28
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 13 (d) 56
  14. 14.What is the 40th term of the AP 16, 20, 24, 28, …? (a) 160 (b) 176 (c) 172 (d) 156
  15. 15.What is the 13th term of the AP 13, 16, 19, 22, …? (a) 49 (b) 36 (c) 52 (d) 39
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 153 (d) 33
  18. 18.Which term of the AP 17, 21, 25, 29, … is 161? (a) 36th (b) 38th (c) 37th (d) 39th
  19. 19.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 140 (b) 70 (c) 19 (d) 73
  20. 20.What is the 15th term of the AP 10, 18, 26, 34, …? (a) 112 (b) 130 (c) 122 (d) 120
  21. 21.What is the 11th term of the AP 20, 24, 28, 32, …? (a) 40 (b) 60 (c) 44 (d) 64
  22. 22.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 98 (b) 50 (c) 10 (d) 49
  23. 23.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 72 (b) 66 (c) 16 (d) 132
  24. 24.What is the 22nd term of the AP 2, 4, 6, 8, …? (a) 46 (b) 45 (c) 44 (d) 42
  25. 25.What is the sum of all the whole numbers from 1 to 89? (a) 4005 (b) 4006 (c) 8010 (d) 3916
  26. 26.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1892 (c) 1830 (d) 1891
  27. 27.What is the missing term in the AP 1, 10, ?, 28, 37? (a) 18 (b) 20 (c) 28 (d) 19
  28. 28.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2592 (c) 5256 (d) 2628
  29. 29.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 396 (b) 209 (c) 28 (d) 198
  30. 30.What is the 26th term of the AP 13, 20, 27, 34, …? (a) 195 (b) 188 (c) 182 (d) 175
  31. 31.What is the 23rd term of the AP 10, 17, 24, 31, …? (a) 161 (b) 164 (c) 171 (d) 154
  32. 32.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 390 (b) 195 (c) 210 (d) 33
  33. 33.What is the 33rd term of the AP 3, 9, 15, 21, …? (a) 195 (b) 198 (c) 192 (d) 201
  34. 34.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 19 (b) 23 (c) 18 (d) 17
  35. 35.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 5 (b) 7 (c) 6 (d) 4
  36. 36.Which term of the AP 14, 16, 18, 20, … is 50? (a) 20th (b) 19th (c) 25th (d) 18th
  37. 37.What is the 11th term of the AP 12, 21, 30, 39, …? (a) 99 (b) 90 (c) 111 (d) 102
  38. 38.What is the sum of all the whole numbers from 1 to 41? (a) 1722 (b) 820 (c) 861 (d) 862
  39. 39.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 6 (b) 10 (c) 5 (d) 7
  40. 40.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 203 (b) 364 (c) 44 (d) 182

Answer key

  1. 86
  2. 205
  3. 15
  4. 561
  5. 625
  6. 28th
  7. 66
  8. 168
  9. 17th
  10. 784
  11. 37
  12. 29
  13. 49
  14. 172
  15. 49
  16. 64
  17. 289
  18. 37th
  19. 70
  20. 122
  21. 60
  22. 49
  23. 66
  24. 44
  25. 4005
  26. 1891
  27. 19
  28. 2628
  29. 198
  30. 188
  31. 164
  32. 195
  33. 195
  34. 18
  35. 5
  36. 19th
  37. 102
  38. 861
  39. 6
  40. 182

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