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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 92 · 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 16th term of the AP 6, 9, 12, 15, …? (a) 45 (b) 51 (c) 48 (d) 54
  2. 2.What is the missing term in the AP 2, 10, 18, ?, 34? (a) 25 (b) 34 (c) 27 (d) 26
  3. 3.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 170 (c) 180 (d) 340
  4. 4.What is the missing term in the AP 8, ?, 14, 17, 20? (a) 12 (b) 11 (c) 14 (d) 10
  5. 5.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 192 (c) 31 (d) 114
  6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 136 (d) 272
  7. 7.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 370 (b) 400 (c) 64 (d) 740
  8. 8.What is the 22nd term of the AP 13, 21, 29, 37, …? (a) 176 (b) 189 (c) 181 (d) 168
  9. 9.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 40 (b) 6 (c) 21 (d) 20
  10. 10.What is the 14th term of the AP 7, 15, 23, 31, …? (a) 112 (b) 104 (c) 111 (d) 119
  11. 11.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4950 (c) 4851 (d) 4951
  12. 12.What is the 16th term of the AP 18, 20, 22, 24, …? (a) 50 (b) 30 (c) 32 (d) 48
  13. 13.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 40 (b) 360 (c) 180 (d) 200
  14. 14.Which term of the AP 12, 15, 18, 21, … is 108? (a) 34th (b) 36th (c) 33rd (d) 32nd
  15. 15.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 30 (b) 220 (c) 231 (d) 440
  16. 16.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 186 (b) 23 (c) 93 (d) 102
  17. 17.What is the 28th term of the AP 11, 16, 21, 26, …? (a) 146 (b) 135 (c) 140 (d) 151
  18. 18.What is the 16th term of the AP 20, 24, 28, 32, …? (a) 84 (b) 64 (c) 80 (d) 60
  19. 19.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 43 (b) 414 (c) 207 (d) 212
  20. 20.What is the 18th term of the AP 2, 4, 6, 8, …? (a) 37 (b) 36 (c) 38 (d) 34
  21. 21.What is the 24th term of the AP 17, 21, 25, 29, …? (a) 92 (b) 113 (c) 109 (d) 96
  22. 22.What is the 39th term of the AP 18, 20, 22, 24, …? (a) 94 (b) 78 (c) 96 (d) 76
  23. 23.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 143 (b) 132 (c) 264 (d) 22
  24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 36 (d) 42
  25. 25.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 812 (d) 784
  26. 26.Which term of the AP 11, 16, 21, 26, … is 91? (a) 17th (b) 19th (c) 16th (d) 18th
  27. 27.What is the 20th term of the AP 15, 20, 25, 30, …? (a) 100 (b) 110 (c) 95 (d) 115
  28. 28.What is the 33rd term of the AP 3, 8, 13, 18, …? (a) 168 (b) 165 (c) 160 (d) 163
  29. 29.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3655 (c) 3698 (d) 3741
  30. 30.Which term of the AP 2, 9, 16, 23, … is 107? (a) 16th (b) 15th (c) 18th (d) 17th
  31. 31.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 2701 (c) 5550 (d) 2775
  32. 32.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 5256 (c) 2628 (d) 2556
  33. 33.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 182 (d) 91
  34. 34.Which term of the AP 5, 7, 9, 11, … is 27? (a) 14th (b) 12th (c) 11th (d) 13th
  35. 35.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 78 (b) 14 (c) 154 (d) 77
  36. 36.What is the 18th term of the AP 12, 16, 20, 24, …? (a) 84 (b) 68 (c) 72 (d) 80
  37. 37.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1129 (c) 1128 (d) 1081
  38. 38.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 75 (b) 150 (c) 80 (d) 25
  39. 39.Which term of the AP 8, 10, 12, 14, … is 32? (a) 14th (b) 12th (c) 13th (d) 16th
  40. 40.What is the 14th term of the AP 14, 23, 32, 41, …? (a) 126 (b) 117 (c) 131 (d) 140

Answer key

  1. 51
  2. 26
  3. 170
  4. 11
  5. 96
  6. 256
  7. 370
  8. 181
  9. 20
  10. 111
  11. 4950
  12. 48
  13. 180
  14. 33rd
  15. 220
  16. 93
  17. 146
  18. 80
  19. 207
  20. 36
  21. 109
  22. 94
  23. 132
  24. 36
  25. 784
  26. 17th
  27. 110
  28. 163
  29. 3741
  30. 16th
  31. 2775
  32. 2628
  33. 169
  34. 12th
  35. 77
  36. 80
  37. 1128
  38. 75
  39. 13th
  40. 131

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