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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 736 · 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 13th term of the AP 8, 10, 12, 14, …? (a) 32 (b) 34 (c) 26 (d) 24
  2. 2.Which term of the AP 20, 28, 36, 44, … is 332? (a) 39th (b) 41st (c) 42nd (d) 40th
  3. 3.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  4. 4.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 50 (d) 55
  5. 5.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 3004 (c) 6006 (d) 2926
  6. 6.What is the 10th term of the AP 12, 14, 16, 18, …? (a) 32 (b) 30 (c) 18 (d) 20
  7. 7.Which term of the AP 10, 16, 22, 28, … is 100? (a) 16th (b) 18th (c) 17th (d) 15th
  8. 8.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 5256 (c) 2556 (d) 2628
  9. 9.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 378 (b) 756 (c) 408 (d) 59
  10. 10.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  11. 11.What is the 24th term of the AP 3, 10, 17, 24, …? (a) 161 (b) 164 (c) 168 (d) 171
  12. 12.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3403 (c) 6972 (d) 3486
  13. 13.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 18 (b) 17 (c) 24 (d) 16
  14. 14.What is the missing term in the AP 18, 21, ?, 27, 30? (a) 23 (b) 25 (c) 27 (d) 24
  15. 15.What is the 17th term of the AP 5, 7, 9, 11, …? (a) 39 (b) 37 (c) 32 (d) 34
  16. 16.What is the 18th term of the AP 18, 24, 30, 36, …? (a) 102 (b) 108 (c) 120 (d) 126
  17. 17.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2016 (c) 4160 (d) 2080
  18. 18.What is the 24th term of the AP 5, 8, 11, 14, …? (a) 77 (b) 74 (c) 72 (d) 69
  19. 19.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1152 (c) 1176 (d) 1128
  20. 20.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 240 (b) 42 (c) 260 (d) 480
  21. 21.What is the 11th term of the AP 6, 11, 16, 21, …? (a) 56 (b) 50 (c) 55 (d) 61
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  23. 23.What is the 26th term of the AP 2, 6, 10, 14, …? (a) 100 (b) 102 (c) 104 (d) 106
  24. 24.Which term of the AP 4, 6, 8, 10, … is 62? (a) 30th (b) 31st (c) 32nd (d) 29th
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
  26. 26.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 1122 (c) 562 (d) 561
  27. 27.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 8372 (c) 4187 (d) 4186
  28. 28.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 19 (b) 182 (c) 98 (d) 91
  29. 29.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 66 (c) 33 (d) 36
  30. 30.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 11 (b) 8 (c) 7 (d) 9
  31. 31.What is the 31st term of the AP 15, 19, 23, 27, …? (a) 124 (b) 135 (c) 139 (d) 120
  32. 32.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 1056 (c) 528 (d) 496
  33. 33.Which term of the AP 4, 11, 18, 25, … is 74? (a) 10th (b) 12th (c) 13th (d) 11th
  34. 34.Which term of the AP 8, 16, 24, 32, … is 256? (a) 34th (b) 32nd (c) 33rd (d) 31st
  35. 35.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 66 (b) 16 (c) 72 (d) 132
  36. 36.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 7832 (d) 3828
  37. 37.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 27 (b) 26 (c) 32 (d) 28
  38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 121 (d) 21
  39. 39.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 39 (d) 210
  40. 40.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 105 (b) 210 (c) 112 (d) 21

Answer key

  1. 32
  2. 40th
  3. 144
  4. 55
  5. 3003
  6. 30
  7. 16th
  8. 2628
  9. 378
  10. 729
  11. 164
  12. 3486
  13. 17
  14. 24
  15. 37
  16. 120
  17. 2080
  18. 74
  19. 1176
  20. 240
  21. 56
  22. 36
  23. 102
  24. 30th
  25. 49
  26. 561
  27. 4186
  28. 91
  29. 33
  30. 8
  31. 135
  32. 528
  33. 11th
  34. 32nd
  35. 66
  36. 3916
  37. 27
  38. 121
  39. 400
  40. 105

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