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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 473 · 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.Which term of the AP 12, 18, 24, 30, … is 96? (a) 15th (b) 17th (c) 16th (d) 14th
  2. 2.What is the 24th term of the AP 20, 22, 24, 26, …? (a) 68 (b) 46 (c) 66 (d) 48
  3. 3.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 504 (b) 1008 (c) 75 (d) 540
  4. 4.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 33 (b) 27 (c) 25 (d) 26
  5. 5.Which term of the AP 15, 21, 27, 33, … is 171? (a) 26th (b) 29th (c) 27th (d) 28th
  6. 6.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2080 (c) 2146 (d) 2145
  7. 7.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 11 (b) 10 (c) 13 (d) 9
  8. 8.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 306 (c) 136 (d) 153
  9. 9.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 10 (b) 11 (c) 14 (d) 12
  10. 10.What is the 28th term of the AP 11, 16, 21, 26, …? (a) 146 (b) 140 (c) 151 (d) 135
  11. 11.Which term of the AP 19, 22, 25, 28, … is 115? (a) 32nd (b) 34th (c) 35th (d) 33rd
  12. 12.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 7140 (c) 3570 (d) 3486
  13. 13.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 110 (b) 15 (c) 105 (d) 210
  14. 14.Which term of the AP 11, 14, 17, 20, … is 35? (a) 8th (b) 9th (c) 11th (d) 10th
  15. 15.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  16. 16.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 72 (b) 12 (c) 144 (d) 73
  17. 17.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 28 (b) 27 (c) 34 (d) 26
  18. 18.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1596 (c) 1540 (d) 1568
  19. 19.What is the 12th term of the AP 13, 15, 17, 19, …? (a) 24 (b) 22 (c) 37 (d) 35
  20. 20.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 6006 (c) 3003 (d) 2926
  21. 21.What is the sum of all the whole numbers from 1 to 80? (a) 6480 (b) 3240 (c) 3200 (d) 3160
  22. 22.Which term of the AP 7, 14, 21, 28, … is 63? (a) 11th (b) 10th (c) 8th (d) 9th
  23. 23.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 126 (b) 252 (c) 30 (d) 140
  24. 24.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 13 (d) 56
  26. 26.What is the 18th term of the AP 5, 9, 13, 17, …? (a) 73 (b) 68 (c) 77 (d) 72
  27. 27.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 27 (b) 170 (c) 90 (d) 85
  28. 28.Which term of the AP 18, 23, 28, 33, … is 103? (a) 20th (b) 18th (c) 19th (d) 17th
  29. 29.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 180 (b) 28 (c) 95 (d) 90
  30. 30.What is the 14th term of the AP 19, 26, 33, 40, …? (a) 117 (b) 98 (c) 110 (d) 91
  31. 31.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 32 (b) 27 (c) 26 (d) 25
  32. 32.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 10 (b) 48 (c) 45 (d) 90
  33. 33.What is the 12th term of the AP 7, 9, 11, 13, …? (a) 24 (b) 31 (c) 29 (d) 22
  34. 34.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 261 (b) 49 (c) 266 (d) 522
  35. 35.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 204 (b) 192 (c) 27 (d) 384
  36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  37. 37.What is the 15th term of the AP 16, 24, 32, 40, …? (a) 128 (b) 112 (c) 136 (d) 120
  38. 38.What is the 37th term of the AP 5, 7, 9, 11, …? (a) 79 (b) 74 (c) 72 (d) 77
  39. 39.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 42 (c) 36 (d) 11
  40. 40.What is the missing term in the AP 12, 16, 20, ?, 28? (a) 24 (b) 28 (c) 25 (d) 23

Answer key

  1. 15th
  2. 66
  3. 504
  4. 26
  5. 27th
  6. 2145
  7. 10
  8. 153
  9. 11
  10. 146
  11. 33rd
  12. 3570
  13. 105
  14. 9th
  15. 25
  16. 72
  17. 27
  18. 1596
  19. 35
  20. 3003
  21. 3240
  22. 9th
  23. 126
  24. 256
  25. 49
  26. 73
  27. 85
  28. 18th
  29. 90
  30. 110
  31. 26
  32. 45
  33. 29
  34. 261
  35. 192
  36. 144
  37. 128
  38. 77
  39. 36
  40. 24

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