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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 792 · 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 55? (a) 3080 (b) 1541 (c) 1540 (d) 1485
  2. 2.Which term of the AP 4, 7, 10, 13, … is 100? (a) 34th (b) 32nd (c) 33rd (d) 35th
  3. 3.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 100 (b) 198 (c) 15 (d) 99
  4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 240 (d) 120
  5. 5.What is the 10th term of the AP 20, 28, 36, 44, …? (a) 100 (b) 72 (c) 92 (d) 80
  6. 6.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 18 (c) 19 (d) 21
  7. 7.What is the 12th term of the AP 20, 29, 38, 47, …? (a) 108 (b) 128 (c) 119 (d) 99
  8. 8.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 84 (b) 18 (c) 91 (d) 168
  9. 9.Which term of the AP 12, 18, 24, 30, … is 168? (a) 28th (b) 29th (c) 26th (d) 27th
  10. 10.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 12 (b) 10 (c) 11 (d) 15
  11. 11.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 120 (b) 21 (c) 224 (d) 112
  12. 12.What is the 24th term of the AP 5, 11, 17, 23, …? (a) 149 (b) 138 (c) 143 (d) 144
  13. 13.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 1596 (c) 3306 (d) 1653
  14. 14.What is the 39th term of the AP 6, 11, 16, 21, …? (a) 195 (b) 196 (c) 201 (d) 190
  15. 15.What is the 12th term of the AP 10, 13, 16, 19, …? (a) 46 (b) 33 (c) 36 (d) 43
  16. 16.Which term of the AP 1, 10, 19, 28, … is 226? (a) 25th (b) 26th (c) 28th (d) 27th
  17. 17.What is the 11th term of the AP 6, 11, 16, 21, …? (a) 55 (b) 56 (c) 50 (d) 61
  18. 18.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 231 (c) 462 (d) 41
  19. 19.Which term of the AP 11, 13, 15, 17, … is 53? (a) 23rd (b) 22nd (c) 24th (d) 21st
  20. 20.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 42 (b) 12 (c) 48 (d) 84
  21. 21.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  22. 22.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 23 (b) 22 (c) 26 (d) 21
  23. 23.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 150 (c) 78 (d) 75
  24. 24.What is the 26th term of the AP 7, 9, 11, 13, …? (a) 59 (b) 57 (c) 52 (d) 50
  25. 25.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 191 (c) 171 (d) 380
  26. 26.What is the 27th term of the AP 2, 7, 12, 17, …? (a) 130 (b) 132 (c) 135 (d) 137
  27. 27.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 4950 (c) 10100 (d) 5050
  28. 28.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 55 (d) 406
  29. 29.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 19 (b) 198 (c) 108 (d) 99
  30. 30.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 440 (b) 473 (c) 70 (d) 880
  31. 31.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2145 (c) 2080 (d) 2146
  32. 32.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 40 (b) 80 (c) 41 (d) 10
  33. 33.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 10 (b) 54 (c) 108 (d) 55
  34. 34.What is the 38th term of the AP 9, 15, 21, 27, …? (a) 228 (b) 237 (c) 222 (d) 231
  35. 35.Which term of the AP 1, 4, 7, 10, … is 76? (a) 25th (b) 26th (c) 28th (d) 27th
  36. 36.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 22 (b) 13 (c) 12 (d) 14
  37. 37.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 27 (b) 25 (c) 28 (d) 26
  38. 38.What is the 17th term of the AP 15, 23, 31, 39, …? (a) 136 (b) 151 (c) 128 (d) 143
  39. 39.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1596 (c) 1540 (d) 3192
  40. 40.What is the 20th term of the AP 15, 18, 21, 24, …? (a) 75 (b) 60 (c) 57 (d) 72

Answer key

  1. 1540
  2. 33rd
  3. 99
  4. 225
  5. 92
  6. 19
  7. 119
  8. 84
  9. 27th
  10. 11
  11. 112
  12. 143
  13. 1653
  14. 196
  15. 43
  16. 26th
  17. 56
  18. 441
  19. 22nd
  20. 42
  21. 256
  22. 22
  23. 75
  24. 57
  25. 190
  26. 132
  27. 5050
  28. 784
  29. 99
  30. 440
  31. 2145
  32. 40
  33. 54
  34. 231
  35. 26th
  36. 13
  37. 26
  38. 143
  39. 1596
  40. 72

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