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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 522 · 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 37th term of the AP 2, 7, 12, 17, …? (a) 180 (b) 185 (c) 182 (d) 187
  2. 2.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  3. 3.What is the missing term in the AP 15, 17, 19, ?, 23? (a) 21 (b) 23 (c) 22 (d) 20
  4. 4.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 38 (b) 30 (c) 28 (d) 29
  5. 5.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 200 (b) 380 (c) 28 (d) 190
  6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 256 (d) 31
  7. 7.What is the 26th term of the AP 8, 11, 14, 17, …? (a) 86 (b) 75 (c) 78 (d) 83
  8. 8.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 595 (c) 1190 (d) 561
  9. 9.What is the missing term in the AP 18, ?, 28, 33, 38? (a) 24 (b) 28 (c) 23 (d) 22
  10. 10.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 54 (b) 30 (c) 27 (d) 7
  11. 11.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4753 (c) 4802 (d) 4851
  12. 12.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 4290 (c) 2146 (d) 2145
  13. 13.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
  14. 14.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 180 (b) 26 (c) 170 (d) 340
  15. 15.What is the 19th term of the AP 19, 23, 27, 31, …? (a) 91 (b) 76 (c) 95 (d) 72
  16. 16.What is the 31st term of the AP 15, 20, 25, 30, …? (a) 170 (b) 155 (c) 150 (d) 165
  17. 17.What is the 24th term of the AP 2, 8, 14, 20, …? (a) 146 (b) 144 (c) 138 (d) 140
  18. 18.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 230 (b) 41 (c) 250 (d) 460
  19. 19.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 34 (b) 144 (c) 129 (d) 258
  20. 20.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 22 (b) 17 (c) 18 (d) 19
  21. 21.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 10 (b) 11 (c) 12 (d) 14
  22. 22.What is the 14th term of the AP 16, 25, 34, 43, …? (a) 142 (b) 117 (c) 133 (d) 126
  23. 23.What is the 21st term of the AP 15, 19, 23, 27, …? (a) 95 (b) 99 (c) 84 (d) 80
  24. 24.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 192 (b) 96 (c) 104 (d) 19
  25. 25.What is the 34th term of the AP 18, 21, 24, 27, …? (a) 117 (b) 102 (c) 99 (d) 120
  26. 26.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 25 (c) 9 (d) 30
  27. 27.What is the missing term in the AP 16, 22, 28, ?, 40? (a) 40 (b) 35 (c) 34 (d) 33
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 110 (d) 19
  29. 29.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 225 (b) 49 (c) 450 (d) 252
  30. 30.Which term of the AP 1, 3, 5, 7, … is 57? (a) 28th (b) 31st (c) 29th (d) 30th
  31. 31.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 990 (c) 968 (d) 1980
  32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  33. 33.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 435 (c) 930 (d) 465
  34. 34.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 13 (b) 90 (c) 85 (d) 170
  35. 35.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 600 (b) 324 (c) 47 (d) 300
  36. 36.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 19 (b) 21 (c) 18 (d) 20
  37. 37.Which term of the AP 8, 13, 18, 23, … is 78? (a) 15th (b) 17th (c) 16th (d) 14th
  38. 38.What is the 34th term of the AP 13, 16, 19, 22, …? (a) 99 (b) 112 (c) 102 (d) 115
  39. 39.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 306 (d) 33
  40. 40.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 23 (b) 17 (c) 16 (d) 15

Answer key

  1. 182
  2. 81
  3. 21
  4. 29
  5. 190
  6. 256
  7. 83
  8. 595
  9. 23
  10. 27
  11. 4851
  12. 2145
  13. 400
  14. 170
  15. 91
  16. 165
  17. 140
  18. 230
  19. 129
  20. 18
  21. 11
  22. 133
  23. 95
  24. 96
  25. 117
  26. 25
  27. 34
  28. 100
  29. 225
  30. 29th
  31. 990
  32. 324
  33. 465
  34. 85
  35. 300
  36. 19
  37. 15th
  38. 112
  39. 289
  40. 16

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