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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 670 · 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, 6, 11, 16, … is 161? (a) 33rd (b) 32nd (c) 34th (d) 35th
  2. 2.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 168 (b) 91 (c) 18 (d) 84
  3. 3.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 13 (c) 63 (d) 126
  4. 4.What is the 18th term of the AP 1, 5, 9, 13, …? (a) 69 (b) 73 (c) 72 (d) 68
  5. 5.What is the 13th term of the AP 20, 24, 28, 32, …? (a) 68 (b) 72 (c) 48 (d) 52
  6. 6.What is the 14th term of the AP 1, 4, 7, 10, …? (a) 39 (b) 42 (c) 43 (d) 40
  7. 7.What is the 35th term of the AP 10, 19, 28, 37, …? (a) 325 (b) 316 (c) 315 (d) 306
  8. 8.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
  9. 9.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 18 (b) 22 (c) 16 (d) 17
  10. 10.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 4560 (c) 4465 (d) 9120
  11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  12. 12.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 272 (c) 120 (d) 128
  13. 13.Which term of the AP 10, 18, 26, 34, … is 146? (a) 17th (b) 18th (c) 20th (d) 19th
  14. 14.Which term of the AP 12, 16, 20, 24, … is 116? (a) 27th (b) 26th (c) 28th (d) 29th
  15. 15.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 31 (b) 240 (c) 252 (d) 480
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  17. 17.What is the 13th term of the AP 16, 20, 24, 28, …? (a) 68 (b) 52 (c) 64 (d) 48
  18. 18.What is the 27th term of the AP 15, 23, 31, 39, …? (a) 216 (b) 208 (c) 223 (d) 231
  19. 19.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 144 (b) 72 (c) 22 (d) 84
  20. 20.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 42 (b) 84 (c) 43 (d) 9
  21. 21.What is the 18th term of the AP 7, 14, 21, 28, …? (a) 119 (b) 127 (c) 126 (d) 133
  22. 22.What is the 20th term of the AP 3, 8, 13, 18, …? (a) 100 (b) 98 (c) 95 (d) 103
  23. 23.What is the 29th term of the AP 5, 12, 19, 26, …? (a) 196 (b) 203 (c) 208 (d) 201
  24. 24.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 252 (b) 225 (c) 450 (d) 49
  25. 25.Which term of the AP 2, 7, 12, 17, … is 122? (a) 24th (b) 27th (c) 25th (d) 26th
  26. 26.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 3906 (c) 1953 (d) 1922
  27. 27.What is the 40th term of the AP 10, 14, 18, 22, …? (a) 160 (b) 170 (c) 156 (d) 166
  28. 28.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2592 (c) 2556 (d) 2628
  29. 29.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 23 (b) 22 (c) 21 (d) 24
  30. 30.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 55 (c) 66 (d) 132
  31. 31.Which term of the AP 17, 23, 29, 35, … is 149? (a) 24th (b) 22nd (c) 23rd (d) 25th
  32. 32.What is the 26th term of the AP 1, 9, 17, 25, …? (a) 208 (b) 201 (c) 209 (d) 200
  33. 33.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 17 (b) 55 (c) 58 (d) 110
  34. 34.What is the 33rd term of the AP 9, 14, 19, 24, …? (a) 160 (b) 174 (c) 165 (d) 169
  35. 35.What is the 17th term of the AP 1, 3, 5, 7, …? (a) 34 (b) 35 (c) 33 (d) 32
  36. 36.What is the 40th term of the AP 15, 21, 27, 33, …? (a) 234 (b) 249 (c) 255 (d) 240
  37. 37.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 703 (c) 1482 (d) 741
  38. 38.Which term of the AP 6, 9, 12, 15, … is 42? (a) 12th (b) 13th (c) 15th (d) 14th
  39. 39.What is the 14th term of the AP 19, 27, 35, 43, …? (a) 131 (b) 104 (c) 112 (d) 123
  40. 40.Which term of the AP 4, 10, 16, 22, … is 232? (a) 41st (b) 39th (c) 40th (d) 38th

Answer key

  1. 33rd
  2. 84
  3. 63
  4. 69
  5. 68
  6. 40
  7. 316
  8. 225
  9. 17
  10. 4560
  11. 25
  12. 136
  13. 18th
  14. 27th
  15. 240
  16. 121
  17. 64
  18. 223
  19. 72
  20. 42
  21. 126
  22. 98
  23. 201
  24. 225
  25. 25th
  26. 1953
  27. 166
  28. 2628
  29. 22
  30. 66
  31. 23rd
  32. 201
  33. 55
  34. 169
  35. 33
  36. 249
  37. 741
  38. 13th
  39. 123
  40. 39th

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