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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 773 · 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 all the whole numbers from 1 to 77? (a) 6006 (b) 3004 (c) 3003 (d) 2926
  2. 2.Which term of the AP 18, 22, 26, 30, … is 94? (a) 19th (b) 20th (c) 21st (d) 22nd
  3. 3.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 800 (c) 820 (d) 1640
  4. 4.Which term of the AP 4, 6, 8, 10, … is 76? (a) 36th (b) 39th (c) 37th (d) 38th
  5. 5.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 180 (b) 174 (c) 348 (d) 20
  6. 6.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 216 (b) 196 (c) 392 (d) 42
  7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  8. 8.Which term of the AP 16, 18, 20, 22, … is 92? (a) 46th (b) 39th (c) 38th (d) 40th
  9. 9.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 4050 (c) 8190 (d) 4095
  10. 10.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 98 (b) 112 (c) 26 (d) 196
  11. 11.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 191 (c) 380 (d) 190
  12. 12.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 37 (b) 368 (c) 200 (d) 184
  13. 13.What is the missing term in the AP 8, 15, ?, 29, 36? (a) 29 (b) 21 (c) 23 (d) 22
  14. 14.What is the 26th term of the AP 8, 17, 26, 35, …? (a) 234 (b) 225 (c) 233 (d) 242
  15. 15.Which term of the AP 12, 18, 24, 30, … is 114? (a) 20th (b) 18th (c) 19th (d) 17th
  16. 16.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 198 (b) 396 (c) 203 (d) 42
  17. 17.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 351 (c) 702 (d) 51
  18. 18.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 240 (b) 220 (c) 45 (d) 440
  19. 19.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 120 (c) 240 (d) 138
  20. 20.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4186 (c) 4095 (d) 8372
  21. 21.What is the 18th term of the AP 20, 25, 30, 35, …? (a) 90 (b) 85 (c) 105 (d) 110
  22. 22.What is the 39th term of the AP 18, 22, 26, 30, …? (a) 174 (b) 152 (c) 156 (d) 170
  23. 23.What is the 32nd term of the AP 5, 13, 21, 29, …? (a) 261 (b) 253 (c) 256 (d) 248
  24. 24.What is the 14th term of the AP 3, 5, 7, 9, …? (a) 29 (b) 26 (c) 31 (d) 28
  25. 25.What is the missing term in the AP 11, 20, ?, 38, 47? (a) 29 (b) 28 (c) 30 (d) 38
  26. 26.What is the 10th term of the AP 1, 6, 11, 16, …? (a) 45 (b) 51 (c) 46 (d) 50
  27. 27.What is the 25th term of the AP 2, 10, 18, 26, …? (a) 200 (b) 192 (c) 194 (d) 202
  28. 28.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 80 (b) 20 (c) 154 (d) 77
  29. 29.What is the sum of all the whole numbers from 1 to 89? (a) 3916 (b) 4006 (c) 4005 (d) 8010
  30. 30.Which term of the AP 10, 17, 24, 31, … is 108? (a) 14th (b) 15th (c) 17th (d) 16th
  31. 31.Which term of the AP 14, 20, 26, 32, … is 92? (a) 13th (b) 16th (c) 15th (d) 14th
  32. 32.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  33. 33.What is the 26th term of the AP 8, 11, 14, 17, …? (a) 78 (b) 86 (c) 75 (d) 83
  34. 34.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 380 (b) 200 (c) 190 (d) 28
  35. 35.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 96 (b) 22 (c) 87 (d) 174
  36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 57 (d) 435
  37. 37.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 1953 (c) 3906 (d) 1922
  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 missing term in the AP 14, ?, 20, 23, 26? (a) 18 (b) 17 (c) 16 (d) 20
  40. 40.What is the 26th term of the AP 17, 22, 27, 32, …? (a) 130 (b) 142 (c) 125 (d) 147

Answer key

  1. 3003
  2. 20th
  3. 820
  4. 37th
  5. 174
  6. 196
  7. 100
  8. 39th
  9. 4095
  10. 98
  11. 190
  12. 184
  13. 22
  14. 233
  15. 18th
  16. 198
  17. 676
  18. 220
  19. 120
  20. 4186
  21. 105
  22. 170
  23. 253
  24. 29
  25. 29
  26. 46
  27. 194
  28. 77
  29. 4005
  30. 15th
  31. 14th
  32. 25
  33. 83
  34. 190
  35. 87
  36. 841
  37. 1953
  38. 780
  39. 17
  40. 142

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