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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 60 · 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 11th term of the AP 19, 26, 33, 40, …? (a) 70 (b) 77 (c) 96 (d) 89
  2. 2.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 20 (b) 220 (c) 120 (d) 110
  3. 3.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 666 (c) 703 (d) 1406
  4. 4.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 22 (b) 21 (c) 23 (d) 20
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 56 (d) 49
  6. 6.What is the 12th term of the AP 17, 26, 35, 44, …? (a) 108 (b) 99 (c) 116 (d) 125
  7. 7.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 188 (b) 376 (c) 41 (d) 208
  8. 8.Which term of the AP 18, 26, 34, 42, … is 266? (a) 34th (b) 33rd (c) 31st (d) 32nd
  9. 9.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 25 (b) 24 (c) 23 (d) 29
  10. 10.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 34 (b) 220 (c) 125 (d) 110
  11. 11.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 156 (b) 168 (c) 312 (d) 30
  12. 12.Which term of the AP 5, 10, 15, 20, … is 100? (a) 21st (b) 19th (c) 20th (d) 22nd
  13. 13.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 8190 (c) 4095 (d) 4050
  14. 14.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 2850 (c) 2775 (d) 5700
  15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
  16. 16.What is the 20th term of the AP 16, 25, 34, 43, …? (a) 196 (b) 180 (c) 171 (d) 187
  17. 17.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 465 (c) 450 (d) 930
  18. 18.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 100 (b) 32 (c) 200 (d) 115
  19. 19.Which term of the AP 1, 4, 7, 10, … is 106? (a) 35th (b) 38th (c) 37th (d) 36th
  20. 20.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 166 (b) 165 (c) 20 (d) 330
  21. 21.What is the 16th term of the AP 8, 11, 14, 17, …? (a) 45 (b) 53 (c) 56 (d) 48
  22. 22.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 242 (c) 253 (d) 506
  23. 23.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 35 (b) 43 (c) 34 (d) 33
  24. 24.Which term of the AP 16, 21, 26, 31, … is 81? (a) 13th (b) 15th (c) 14th (d) 16th
  25. 25.What is the 24th term of the AP 9, 15, 21, 27, …? (a) 153 (b) 147 (c) 144 (d) 138
  26. 26.What is the sum of all the whole numbers from 1 to 79? (a) 6320 (b) 3161 (c) 3081 (d) 3160
  27. 27.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 68 (b) 420 (c) 840 (d) 456
  28. 28.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 4560 (c) 9120 (d) 4561
  29. 29.What is the missing term in the AP 2, 10, 18, ?, 34? (a) 34 (b) 25 (c) 26 (d) 27
  30. 30.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 216 (b) 108 (c) 33 (d) 126
  31. 31.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 407 (b) 440 (c) 67 (d) 814
  32. 32.What is the 11th term of the AP 16, 20, 24, 28, …? (a) 56 (b) 60 (c) 44 (d) 40
  33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 39 (d) 420
  34. 34.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 78 (d) 144
  35. 35.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 396 (b) 198 (c) 33 (d) 201
  36. 36.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 1640 (c) 800 (d) 780
  37. 37.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 450 (b) 36 (c) 240 (d) 225
  38. 38.Which term of the AP 7, 14, 21, 28, … is 217? (a) 33rd (b) 31st (c) 32nd (d) 30th
  39. 39.Which term of the AP 20, 29, 38, 47, … is 128? (a) 15th (b) 12th (c) 13th (d) 14th
  40. 40.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 290 (b) 320 (c) 56 (d) 580

Answer key

  1. 89
  2. 110
  3. 703
  4. 21
  5. 49
  6. 116
  7. 188
  8. 32nd
  9. 24
  10. 110
  11. 156
  12. 20th
  13. 4095
  14. 2850
  15. 36
  16. 187
  17. 465
  18. 100
  19. 36th
  20. 165
  21. 53
  22. 253
  23. 34
  24. 14th
  25. 147
  26. 3160
  27. 420
  28. 4560
  29. 26
  30. 108
  31. 407
  32. 56
  33. 400
  34. 144
  35. 198
  36. 820
  37. 225
  38. 31st
  39. 13th
  40. 290

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