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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 375 · 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 36th term of the AP 3, 12, 21, 30, …? (a) 327 (b) 315 (c) 324 (d) 318
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  3. 3.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 256 (d) 272
  4. 4.What is the 32nd term of the AP 5, 10, 15, 20, …? (a) 165 (b) 155 (c) 161 (d) 160
  5. 5.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 16 (b) 60 (c) 120 (d) 65
  6. 6.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 80 (b) 40 (c) 12 (d) 45
  7. 7.What is the missing term in the AP 2, 4, 6, ?, 10? (a) 7 (b) 10 (c) 9 (d) 8
  8. 8.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 340 (c) 61 (d) 370
  9. 9.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2557 (c) 2485 (d) 5112
  10. 10.What is the sum of all the whole numbers from 1 to 90? (a) 8190 (b) 4005 (c) 4050 (d) 4095
  11. 11.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 8 (b) 7 (c) 11 (d) 9
  12. 12.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 9900 (c) 4851 (d) 4951
  13. 13.What is the 18th term of the AP 4, 11, 18, 25, …? (a) 130 (b) 119 (c) 123 (d) 126
  14. 14.What is the 14th term of the AP 5, 8, 11, 14, …? (a) 47 (b) 39 (c) 44 (d) 42
  15. 15.What is the sum of all the whole numbers from 1 to 87? (a) 7656 (b) 3828 (c) 3741 (d) 3829
  16. 16.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 784 (d) 812
  17. 17.What is the missing term in the AP 10, ?, 22, 28, 34? (a) 15 (b) 17 (c) 22 (d) 16
  18. 18.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 432 (b) 240 (c) 216 (d) 48
  19. 19.Which term of the AP 12, 16, 20, 24, … is 108? (a) 24th (b) 25th (c) 27th (d) 26th
  20. 20.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 23 (b) 25 (c) 24 (d) 29
  21. 21.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 28 (b) 37 (c) 29 (d) 27
  22. 22.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 7 (b) 27 (c) 30 (d) 54
  23. 23.Which term of the AP 16, 20, 24, 28, … is 76? (a) 19th (b) 15th (c) 17th (d) 16th
  24. 24.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 150 (c) 12 (d) 75
  25. 25.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 25 (b) 18 (c) 19 (d) 17
  26. 26.Which term of the AP 2, 7, 12, 17, … is 92? (a) 18th (b) 19th (c) 21st (d) 20th
  27. 27.What is the 39th term of the AP 20, 23, 26, 29, …? (a) 117 (b) 134 (c) 114 (d) 137
  28. 28.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 18 (b) 19 (c) 26 (d) 17
  29. 29.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 25 (b) 26 (c) 29 (d) 27
  30. 30.What is the 20th term of the AP 12, 16, 20, 24, …? (a) 92 (b) 88 (c) 80 (d) 76
  31. 31.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4371 (c) 8930 (d) 4418
  32. 32.Which term of the AP 11, 19, 27, 35, … is 75? (a) 9th (b) 11th (c) 8th (d) 10th
  33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  34. 34.What is the 31st term of the AP 13, 18, 23, 28, …? (a) 150 (b) 163 (c) 155 (d) 168
  35. 35.What is the 30th term of the AP 9, 18, 27, 36, …? (a) 279 (b) 261 (c) 271 (d) 270
  36. 36.What is the 10th term of the AP 15, 19, 23, 27, …? (a) 40 (b) 55 (c) 36 (d) 51
  37. 37.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 31 (b) 29 (c) 30 (d) 35
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 210 (d) 39
  39. 39.What is the 26th term of the AP 3, 8, 13, 18, …? (a) 133 (b) 125 (c) 130 (d) 128
  40. 40.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 60 (b) 61 (c) 14 (d) 120

Answer key

  1. 318
  2. 64
  3. 256
  4. 160
  5. 60
  6. 40
  7. 8
  8. 340
  9. 2556
  10. 4095
  11. 8
  12. 4950
  13. 123
  14. 44
  15. 3828
  16. 784
  17. 16
  18. 216
  19. 25th
  20. 24
  21. 28
  22. 27
  23. 16th
  24. 75
  25. 18
  26. 19th
  27. 134
  28. 18
  29. 26
  30. 88
  31. 4465
  32. 9th
  33. 144
  34. 163
  35. 270
  36. 51
  37. 30
  38. 400
  39. 128
  40. 60

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