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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 191 · 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 8 terms of the AP 2, 4, 6, …? (a) 16 (b) 144 (c) 80 (d) 72
  2. 2.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 43 (b) 200 (c) 352 (d) 176
  3. 3.What is the 26th term of the AP 1, 10, 19, 28, …? (a) 234 (b) 225 (c) 235 (d) 226
  4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  5. 5.What is the missing term in the AP 10, ?, 28, 37, 46? (a) 18 (b) 20 (c) 28 (d) 19
  6. 6.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 12 (b) 14 (c) 10 (d) 11
  7. 7.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 4560 (c) 4561 (d) 9120
  8. 8.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 20 (b) 140 (c) 70 (d) 73
  9. 9.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 650 (b) 325 (c) 350 (d) 55
  10. 10.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 105 (c) 120 (d) 121
  11. 11.What is the 11th term of the AP 19, 28, 37, 46, …? (a) 109 (b) 99 (c) 90 (d) 118
  12. 12.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 2162 (c) 1081 (d) 1058
  13. 13.What is the 34th term of the AP 10, 13, 16, 19, …? (a) 112 (b) 99 (c) 102 (d) 109
  14. 14.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 780 (c) 1640 (d) 820
  15. 15.What is the 28th term of the AP 3, 7, 11, 15, …? (a) 111 (b) 115 (c) 112 (d) 108
  16. 16.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 11 (c) 70 (d) 65
  17. 17.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1226 (c) 2450 (d) 1225
  18. 18.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 780 (d) 781
  19. 19.Which term of the AP 18, 26, 34, 42, … is 130? (a) 16th (b) 17th (c) 14th (d) 15th
  20. 20.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 63 (b) 396 (c) 363 (d) 726
  21. 21.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 4830 (c) 2415 (d) 2416
  22. 22.What is the 21st term of the AP 10, 14, 18, 22, …? (a) 94 (b) 80 (c) 90 (d) 84
  23. 23.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  24. 24.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 102 (b) 25 (c) 180 (d) 90
  25. 25.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 13 (b) 20 (c) 15 (d) 14
  26. 26.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5000 (c) 5050 (d) 10100
  27. 27.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 930 (c) 465 (d) 900
  28. 28.Which term of the AP 2, 8, 14, 20, … is 50? (a) 10th (b) 8th (c) 11th (d) 9th
  29. 29.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 15 (b) 16 (c) 17 (d) 20
  30. 30.What is the 18th term of the AP 2, 9, 16, 23, …? (a) 119 (b) 121 (c) 126 (d) 128
  31. 31.Which term of the AP 15, 20, 25, 30, … is 100? (a) 20th (b) 18th (c) 17th (d) 19th
  32. 32.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 63 (c) 11 (d) 64
  33. 33.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 42 (b) 396 (c) 198 (d) 203
  34. 34.What is the 28th term of the AP 6, 8, 10, 12, …? (a) 62 (b) 54 (c) 56 (d) 60
  35. 35.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 912 (b) 456 (c) 492 (d) 71
  36. 36.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 132 (c) 66 (d) 55
  37. 37.What is the 37th term of the AP 1, 3, 5, 7, …? (a) 72 (b) 75 (c) 74 (d) 73
  38. 38.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 18 (b) 13 (c) 15 (d) 14
  39. 39.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 8372 (c) 4095 (d) 4186
  40. 40.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 5700 (c) 2850 (d) 2851

Answer key

  1. 72
  2. 176
  3. 226
  4. 100
  5. 19
  6. 11
  7. 4560
  8. 70
  9. 325
  10. 120
  11. 109
  12. 1081
  13. 109
  14. 820
  15. 111
  16. 65
  17. 1225
  18. 780
  19. 15th
  20. 363
  21. 2415
  22. 90
  23. 400
  24. 90
  25. 14
  26. 5050
  27. 900
  28. 9th
  29. 16
  30. 121
  31. 18th
  32. 63
  33. 198
  34. 60
  35. 456
  36. 66
  37. 73
  38. 14
  39. 4186
  40. 2850

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