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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 730 · 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 the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 42 (d) 21
  2. 2.What is the 28th term of the AP 13, 22, 31, 40, …? (a) 243 (b) 256 (c) 265 (d) 252
  3. 3.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 33 (b) 168 (c) 304 (d) 152
  4. 4.What is the 10th term of the AP 1, 8, 15, 22, …? (a) 70 (b) 63 (c) 64 (d) 71
  5. 5.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 408 (b) 67 (c) 816 (d) 444
  6. 6.What is the 23rd term of the AP 14, 21, 28, 35, …? (a) 175 (b) 161 (c) 168 (d) 154
  7. 7.Which term of the AP 5, 7, 9, 11, … is 79? (a) 37th (b) 39th (c) 38th (d) 40th
  8. 8.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 180 (b) 30 (c) 330 (d) 165
  9. 9.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 24 (b) 6 (c) 42 (d) 21
  10. 10.Which term of the AP 5, 10, 15, 20, … is 140? (a) 30th (b) 28th (c) 29th (d) 27th
  11. 11.Which term of the AP 15, 23, 31, 39, … is 95? (a) 12th (b) 11th (c) 13th (d) 10th
  12. 12.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 330 (c) 300 (d) 600
  13. 13.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 15 (b) 126 (c) 63 (d) 70
  14. 14.Which term of the AP 19, 22, 25, 28, … is 109? (a) 30th (b) 32nd (c) 33rd (d) 31st
  15. 15.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 305 (b) 330 (c) 53 (d) 610
  16. 16.What is the missing term in the AP 16, 19, 22, ?, 28? (a) 24 (b) 26 (c) 28 (d) 25
  17. 17.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 43 (b) 14 (c) 40 (d) 80
  18. 18.Which term of the AP 5, 8, 11, 14, … is 26? (a) 7th (b) 8th (c) 10th (d) 9th
  19. 19.What is the 33rd term of the AP 16, 18, 20, 22, …? (a) 64 (b) 80 (c) 66 (d) 82
  20. 20.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 66 (d) 21
  22. 22.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 13 (b) 11 (c) 10 (d) 9
  23. 23.Which term of the AP 9, 16, 23, 30, … is 65? (a) 10th (b) 8th (c) 11th (d) 9th
  24. 24.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 39 (b) 41 (c) 49 (d) 40
  25. 25.Which term of the AP 13, 18, 23, 28, … is 73? (a) 14th (b) 15th (c) 12th (d) 13th
  26. 26.What is the sum of all the whole numbers from 1 to 15? (a) 120 (b) 121 (c) 105 (d) 240
  27. 27.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 17 (b) 20 (c) 16 (d) 15
  28. 28.Which term of the AP 2, 9, 16, 23, … is 58? (a) 10th (b) 9th (c) 11th (d) 8th
  29. 29.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 14 (b) 12 (c) 16 (d) 13
  30. 30.Which term of the AP 7, 9, 11, 13, … is 23? (a) 11th (b) 8th (c) 10th (d) 9th
  31. 31.Which term of the AP 20, 22, 24, 26, … is 76? (a) 28th (b) 38th (c) 29th (d) 30th
  32. 32.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 210 (b) 195 (c) 33 (d) 390
  33. 33.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 135 (b) 138 (c) 270 (d) 27
  34. 34.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 150 (b) 18 (c) 156 (d) 300
  35. 35.What is the 27th term of the AP 12, 14, 16, 18, …? (a) 64 (b) 52 (c) 66 (d) 54
  36. 36.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 24 (b) 19 (c) 20 (d) 21
  37. 37.Which term of the AP 4, 11, 18, 25, … is 221? (a) 34th (b) 31st (c) 32nd (d) 33rd
  38. 38.Which term of the AP 20, 27, 34, 41, … is 132? (a) 18th (b) 19th (c) 16th (d) 17th
  39. 39.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 6006 (c) 3003 (d) 2926
  40. 40.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 624 (b) 312 (c) 336 (d) 48

Answer key

  1. 36
  2. 256
  3. 152
  4. 64
  5. 408
  6. 168
  7. 38th
  8. 165
  9. 21
  10. 28th
  11. 11th
  12. 300
  13. 63
  14. 31st
  15. 305
  16. 25
  17. 40
  18. 8th
  19. 80
  20. 100
  21. 121
  22. 10
  23. 9th
  24. 40
  25. 13th
  26. 120
  27. 16
  28. 9th
  29. 13
  30. 9th
  31. 29th
  32. 195
  33. 135
  34. 150
  35. 64
  36. 20
  37. 32nd
  38. 17th
  39. 3003
  40. 312

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