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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 187 · 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 all the whole numbers from 1 to 74? (a) 2775 (b) 5550 (c) 2701 (d) 2738
  2. 2.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 930 (d) 465
  3. 3.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 1458 (c) 2970 (d) 1431
  4. 4.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 256 (b) 232 (c) 50 (d) 464
  5. 5.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 812 (d) 784
  6. 6.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 288 (c) 300 (d) 276
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 36 (d) 72
  8. 8.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 1653 (c) 3306 (d) 1596
  9. 9.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 322 (b) 161 (c) 38 (d) 166
  10. 10.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 28 (c) 93 (d) 186
  11. 11.Which term of the AP 12, 15, 18, 21, … is 69? (a) 21st (b) 23rd (c) 20th (d) 19th
  12. 12.What is the 13th term of the AP 6, 9, 12, 15, …? (a) 39 (b) 36 (c) 42 (d) 45
  13. 13.Which term of the AP 15, 19, 23, 27, … is 87? (a) 20th (b) 18th (c) 21st (d) 19th
  14. 14.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 16 (b) 15 (c) 14 (d) 24
  15. 15.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  16. 16.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 496 (c) 528 (d) 1056
  17. 17.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 30 (b) 36 (c) 29 (d) 31
  18. 18.Which term of the AP 6, 12, 18, 24, … is 102? (a) 18th (b) 17th (c) 16th (d) 19th
  19. 19.What is the missing term in the AP 5, 9, 13, ?, 21? (a) 21 (b) 17 (c) 18 (d) 16
  20. 20.Which term of the AP 8, 15, 22, 29, … is 78? (a) 13th (b) 12th (c) 11th (d) 10th
  21. 21.What is the 11th term of the AP 6, 15, 24, 33, …? (a) 96 (b) 105 (c) 90 (d) 99
  22. 22.What is the 10th term of the AP 15, 20, 25, 30, …? (a) 45 (b) 60 (c) 65 (d) 50
  23. 23.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 110 (c) 120 (d) 20
  24. 24.What is the sum of all the whole numbers from 1 to 79? (a) 6320 (b) 3160 (c) 3081 (d) 3161
  25. 25.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 306 (b) 55 (c) 558 (d) 279
  26. 26.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 42 (b) 49 (c) 45 (d) 46
  27. 27.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 310 (b) 51 (c) 570 (d) 285
  28. 28.What is the missing term in the AP 8, ?, 26, 35, 44? (a) 17 (b) 18 (c) 26 (d) 16
  29. 29.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 90 (c) 45 (d) 17
  30. 30.Which term of the AP 15, 18, 21, 24, … is 42? (a) 11th (b) 14th (c) 9th (d) 10th
  31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  32. 32.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 50 (c) 55 (d) 110
  33. 33.Which term of the AP 9, 17, 25, 33, … is 225? (a) 30th (b) 27th (c) 28th (d) 29th
  34. 34.Which term of the AP 17, 25, 33, 41, … is 129? (a) 14th (b) 16th (c) 17th (d) 15th
  35. 35.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 9 (b) 8 (c) 10 (d) 12
  36. 36.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 222 (b) 126 (c) 111 (d) 31
  37. 37.What is the 19th term of the AP 6, 15, 24, 33, …? (a) 168 (b) 171 (c) 162 (d) 177
  38. 38.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 39 (b) 420 (c) 230 (d) 210
  39. 39.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 210 (b) 228 (c) 420 (d) 34
  40. 40.What is the 27th term of the AP 20, 27, 34, 41, …? (a) 202 (b) 189 (c) 209 (d) 182

Answer key

  1. 2775
  2. 900
  3. 1485
  4. 232
  5. 784
  6. 300
  7. 64
  8. 1653
  9. 161
  10. 93
  11. 20th
  12. 42
  13. 19th
  14. 15
  15. 25
  16. 528
  17. 30
  18. 17th
  19. 17
  20. 11th
  21. 96
  22. 60
  23. 110
  24. 3160
  25. 279
  26. 46
  27. 285
  28. 17
  29. 45
  30. 10th
  31. 841
  32. 55
  33. 28th
  34. 15th
  35. 9
  36. 111
  37. 168
  38. 210
  39. 210
  40. 202

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