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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 992 · 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 missing term in the AP 1, 3, 5, ?, 9? (a) 8 (b) 6 (c) 9 (d) 7
  2. 2.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 18 (b) 20 (c) 19 (d) 21
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 120 (c) 240 (d) 29
  4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 55 (d) 406
  5. 5.What is the 21st term of the AP 2, 7, 12, 17, …? (a) 100 (b) 105 (c) 102 (d) 107
  6. 6.Which term of the AP 9, 12, 15, 18, … is 51? (a) 14th (b) 17th (c) 16th (d) 15th
  7. 7.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 506 (d) 253
  8. 8.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 12 (b) 51 (c) 50 (d) 100
  9. 9.What is the 27th term of the AP 9, 11, 13, 15, …? (a) 61 (b) 52 (c) 54 (d) 63
  10. 10.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 23 (b) 18 (c) 17 (d) 19
  11. 11.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 21 (b) 87 (c) 84 (d) 168
  12. 12.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 17 (b) 15 (c) 16 (d) 14
  13. 13.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 92 (b) 96 (c) 15 (d) 184
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 15 (d) 64
  15. 15.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 81 (d) 17
  16. 16.What is the 15th term of the AP 13, 20, 27, 34, …? (a) 118 (b) 105 (c) 111 (d) 98
  17. 17.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 340 (c) 370 (d) 61
  18. 18.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 21 (b) 22 (c) 19 (d) 20
  19. 19.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 136 (d) 154
  20. 20.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 75 (b) 23 (c) 150 (d) 85
  21. 21.What is the 28th term of the AP 6, 12, 18, 24, …? (a) 162 (b) 169 (c) 168 (d) 174
  22. 22.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 484 (b) 242 (c) 264 (d) 42
  23. 23.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 40 (b) 180 (c) 350 (d) 175
  24. 24.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 110 (b) 20 (c) 220 (d) 120
  25. 25.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 182 (d) 169
  26. 26.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 55 (d) 50
  27. 27.What is the 12th term of the AP 4, 12, 20, 28, …? (a) 96 (b) 100 (c) 88 (d) 92
  28. 28.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 704 (c) 703 (d) 666
  29. 29.What is the 12th term of the AP 6, 12, 18, 24, …? (a) 66 (b) 78 (c) 72 (d) 73
  30. 30.What is the 39th term of the AP 1, 5, 9, 13, …? (a) 156 (b) 153 (c) 152 (d) 157
  31. 31.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 120 (b) 132 (c) 240 (d) 30
  32. 32.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 272 (c) 128 (d) 136
  33. 33.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 252 (b) 126 (c) 140 (d) 30
  34. 34.Which term of the AP 3, 9, 15, 21, … is 63? (a) 10th (b) 11th (c) 12th (d) 13th
  35. 35.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 70 (b) 65 (c) 130 (d) 17
  36. 36.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 4656 (c) 4608 (d) 9312
  37. 37.What is the missing term in the AP 12, 18, ?, 30, 36? (a) 23 (b) 25 (c) 30 (d) 24
  38. 38.Which term of the AP 20, 26, 32, 38, … is 146? (a) 24th (b) 23rd (c) 22nd (d) 21st
  39. 39.What is the 33rd term of the AP 2, 7, 12, 17, …? (a) 167 (b) 160 (c) 165 (d) 162
  40. 40.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 10 (c) 90 (d) 45

Answer key

  1. 7
  2. 19
  3. 225
  4. 784
  5. 102
  6. 15th
  7. 484
  8. 50
  9. 61
  10. 18
  11. 84
  12. 15
  13. 92
  14. 64
  15. 81
  16. 111
  17. 340
  18. 20
  19. 153
  20. 75
  21. 168
  22. 242
  23. 175
  24. 110
  25. 169
  26. 55
  27. 92
  28. 703
  29. 72
  30. 153
  31. 120
  32. 136
  33. 126
  34. 11th
  35. 65
  36. 4656
  37. 24
  38. 22nd
  39. 162
  40. 45

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