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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 467 · 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 5 terms of the AP 8, 10, 12, …? (a) 16 (b) 60 (c) 65 (d) 120
  2. 2.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 650 (d) 325
  3. 3.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 91 (d) 25
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
  5. 5.Which term of the AP 12, 17, 22, 27, … is 67? (a) 13th (b) 14th (c) 11th (d) 12th
  6. 6.What is the 36th term of the AP 8, 14, 20, 26, …? (a) 224 (b) 218 (c) 216 (d) 210
  7. 7.What is the 18th term of the AP 7, 12, 17, 22, …? (a) 92 (b) 97 (c) 90 (d) 85
  8. 8.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 272 (d) 31
  9. 9.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 53 (b) 610 (c) 305 (d) 330
  10. 10.What is the 21st term of the AP 1, 3, 5, 7, …? (a) 41 (b) 43 (c) 40 (d) 42
  11. 11.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 35 (b) 44 (c) 34 (d) 36
  12. 12.What is the 15th term of the AP 14, 22, 30, 38, …? (a) 126 (b) 120 (c) 134 (d) 112
  13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 81 (d) 17
  14. 14.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 28 (b) 21 (c) 20 (d) 19
  15. 15.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 75 (b) 12 (c) 150 (d) 80
  16. 16.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 33 (c) 66 (d) 36
  17. 17.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 168 (b) 312 (c) 156 (d) 24
  18. 18.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 862 (c) 1722 (d) 820
  19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 190 (c) 37 (d) 361
  20. 20.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 28 (b) 160 (c) 145 (d) 290
  21. 21.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 28 (b) 26 (c) 27 (d) 36
  22. 22.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 50 (b) 10 (c) 98 (d) 49
  23. 23.What is the 15th term of the AP 1, 5, 9, 13, …? (a) 61 (b) 56 (c) 60 (d) 57
  24. 24.What is the 38th term of the AP 20, 29, 38, 47, …? (a) 353 (b) 362 (c) 342 (d) 333
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 19 (d) 110
  26. 26.What is the 12th term of the AP 6, 15, 24, 33, …? (a) 108 (b) 99 (c) 105 (d) 114
  27. 27.What is the missing term in the AP 19, ?, 25, 28, 31? (a) 23 (b) 21 (c) 25 (d) 22
  28. 28.Which term of the AP 9, 17, 25, 33, … is 209? (a) 27th (b) 25th (c) 28th (d) 26th
  29. 29.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 11 (b) 9 (c) 10 (d) 18
  30. 30.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 27 (b) 192 (c) 204 (d) 384
  31. 31.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 378 (b) 33 (c) 192 (d) 189
  32. 32.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 820 (c) 780 (d) 800
  33. 33.What is the 33rd term of the AP 20, 24, 28, 32, …? (a) 128 (b) 148 (c) 152 (d) 132
  34. 34.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 132 (c) 55 (d) 67
  35. 35.Which term of the AP 16, 23, 30, 37, … is 86? (a) 13th (b) 12th (c) 11th (d) 10th
  36. 36.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 38 (b) 253 (c) 506 (d) 256
  37. 37.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 12 (b) 8 (c) 10 (d) 9
  38. 38.What is the 27th term of the AP 2, 10, 18, 26, …? (a) 216 (b) 218 (c) 210 (d) 208
  39. 39.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 28 (b) 22 (c) 21 (d) 23
  40. 40.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 3 (b) 5 (c) 4 (d) 6

Answer key

  1. 60
  2. 625
  3. 169
  4. 25
  5. 12th
  6. 218
  7. 92
  8. 256
  9. 305
  10. 41
  11. 35
  12. 126
  13. 81
  14. 20
  15. 75
  16. 33
  17. 156
  18. 861
  19. 361
  20. 145
  21. 27
  22. 49
  23. 57
  24. 353
  25. 100
  26. 105
  27. 22
  28. 26th
  29. 10
  30. 192
  31. 189
  32. 820
  33. 148
  34. 66
  35. 11th
  36. 253
  37. 9
  38. 210
  39. 22
  40. 4

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