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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 87 · 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 2, 6, 10, 14, … is 70? (a) 20th (b) 17th (c) 19th (d) 18th
  2. 2.What is the 25th term of the AP 4, 6, 8, 10, …? (a) 50 (b) 48 (c) 54 (d) 52
  3. 3.What is the missing term in the AP 20, 24, 28, ?, 36? (a) 36 (b) 32 (c) 33 (d) 31
  4. 4.What is the missing term in the AP 5, 10, ?, 20, 25? (a) 20 (b) 15 (c) 14 (d) 16
  5. 5.What is the missing term in the AP 16, 19, ?, 25, 28? (a) 22 (b) 21 (c) 23 (d) 25
  6. 6.What is the 38th term of the AP 7, 10, 13, 16, …? (a) 111 (b) 114 (c) 118 (d) 121
  7. 7.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 4692 (c) 2346 (d) 2278
  8. 8.What is the 12th term of the AP 9, 14, 19, 24, …? (a) 69 (b) 60 (c) 64 (d) 55
  9. 9.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 45 (b) 540 (c) 290 (d) 270
  10. 10.What is the 21st term of the AP 7, 13, 19, 25, …? (a) 133 (b) 127 (c) 126 (d) 120
  11. 11.What is the 19th term of the AP 15, 19, 23, 27, …? (a) 91 (b) 76 (c) 87 (d) 72
  12. 12.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 374 (b) 27 (c) 187 (d) 198
  13. 13.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 506 (c) 231 (d) 253
  14. 14.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 19 (b) 24 (c) 21 (d) 20
  15. 15.Which term of the AP 3, 11, 19, 27, … is 115? (a) 17th (b) 14th (c) 15th (d) 16th
  16. 16.What is the missing term in the AP 12, 19, ?, 33, 40? (a) 25 (b) 27 (c) 33 (d) 26
  17. 17.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 936 (b) 468 (c) 72 (d) 504
  18. 18.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 187 (b) 352 (c) 176 (d) 26
  19. 19.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4753 (c) 9506 (d) 4656
  20. 20.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 882 (c) 1806 (d) 903
  21. 21.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 34 (b) 32 (c) 33 (d) 42
  22. 22.What is the 31st term of the AP 5, 7, 9, 11, …? (a) 62 (b) 65 (c) 60 (d) 67
  23. 23.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 31 (b) 32 (c) 33 (d) 41
  24. 24.What is the 11th term of the AP 10, 15, 20, 25, …? (a) 50 (b) 55 (c) 60 (d) 65
  25. 25.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 25 (b) 35 (c) 26 (d) 27
  26. 26.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 418 (b) 34 (c) 209 (d) 212
  27. 27.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 370 (c) 340 (d) 61
  28. 28.What is the 19th term of the AP 8, 15, 22, 29, …? (a) 133 (b) 126 (c) 134 (d) 141
  29. 29.What is the 23rd term of the AP 1, 8, 15, 22, …? (a) 162 (b) 155 (c) 161 (d) 154
  30. 30.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 300 (d) 576
  31. 31.What is the 11th term of the AP 5, 13, 21, 29, …? (a) 88 (b) 80 (c) 85 (d) 93
  32. 32.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 210 (d) 420
  33. 33.Which term of the AP 19, 26, 33, 40, … is 82? (a) 12th (b) 11th (c) 10th (d) 9th
  34. 34.Which term of the AP 20, 25, 30, 35, … is 180? (a) 34th (b) 36th (c) 32nd (d) 33rd
  35. 35.What is the 37th term of the AP 5, 7, 9, 11, …? (a) 74 (b) 77 (c) 72 (d) 79
  36. 36.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 5 (b) 3 (c) 7 (d) 4
  37. 37.Which term of the AP 5, 7, 9, 11, … is 27? (a) 14th (b) 12th (c) 11th (d) 13th
  38. 38.What is the 37th term of the AP 12, 17, 22, 27, …? (a) 185 (b) 197 (c) 180 (d) 192
  39. 39.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 39 (b) 414 (c) 225 (d) 207
  40. 40.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 38 (b) 30 (c) 31 (d) 32

Answer key

  1. 18th
  2. 52
  3. 32
  4. 15
  5. 22
  6. 118
  7. 2346
  8. 64
  9. 270
  10. 127
  11. 87
  12. 187
  13. 253
  14. 20
  15. 15th
  16. 26
  17. 468
  18. 176
  19. 4753
  20. 903
  21. 33
  22. 65
  23. 32
  24. 60
  25. 26
  26. 209
  27. 340
  28. 134
  29. 155
  30. 576
  31. 85
  32. 400
  33. 10th
  34. 33rd
  35. 77
  36. 4
  37. 12th
  38. 192
  39. 207
  40. 31

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