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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 939 · 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 42? (a) 1806 (b) 861 (c) 882 (d) 903
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 15 (d) 64
  3. 3.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 136 (b) 124 (c) 26 (d) 248
  4. 4.Which term of the AP 1, 6, 11, 16, … is 146? (a) 31st (b) 29th (c) 30th (d) 32nd
  5. 5.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 406 (c) 436 (d) 435
  6. 6.What is the missing term in the AP 9, 14, ?, 24, 29? (a) 18 (b) 20 (c) 19 (d) 24
  7. 7.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 420 (b) 39 (c) 230 (d) 210
  8. 8.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 12 (b) 60 (c) 57 (d) 114
  9. 9.Which term of the AP 5, 8, 11, 14, … is 35? (a) 13th (b) 12th (c) 11th (d) 10th
  10. 10.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3003 (c) 6162 (d) 3081
  11. 11.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 210 (c) 105 (d) 114
  12. 12.What is the 10th term of the AP 2, 4, 6, 8, …? (a) 22 (b) 18 (c) 20 (d) 21
  13. 13.What is the 32nd term of the AP 6, 9, 12, 15, …? (a) 99 (b) 93 (c) 96 (d) 102
  14. 14.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 256 (b) 464 (c) 50 (d) 232
  15. 15.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 182 (c) 78 (d) 92
  16. 16.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 16 (b) 50 (c) 100 (d) 53
  17. 17.Which term of the AP 2, 8, 14, 20, … is 68? (a) 12th (b) 13th (c) 14th (d) 11th
  18. 18.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 168 (b) 312 (c) 24 (d) 156
  19. 19.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 9 (b) 39 (c) 42 (d) 78
  20. 20.Which term of the AP 16, 19, 22, 25, … is 121? (a) 37th (b) 35th (c) 38th (d) 36th
  21. 21.Which term of the AP 19, 26, 33, 40, … is 117? (a) 14th (b) 15th (c) 16th (d) 17th
  22. 22.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 56 (b) 320 (c) 290 (d) 580
  23. 23.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 162 (b) 90 (c) 21 (d) 81
  24. 24.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 392 (c) 812 (d) 406
  25. 25.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 120 (b) 11 (c) 64 (d) 60
  26. 26.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
  27. 27.What is the 22nd term of the AP 5, 13, 21, 29, …? (a) 176 (b) 168 (c) 173 (d) 181
  28. 28.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 14 (b) 69 (c) 72 (d) 138
  29. 29.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 220 (b) 418 (c) 209 (d) 29
  30. 30.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 11 (b) 18 (c) 10 (d) 9
  31. 31.Which term of the AP 4, 7, 10, 13, … is 97? (a) 31st (b) 33rd (c) 34th (d) 32nd
  32. 32.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 10 (b) 45 (c) 48 (d) 90
  33. 33.What is the 19th term of the AP 5, 10, 15, 20, …? (a) 95 (b) 96 (c) 90 (d) 100
  34. 34.What is the missing term in the AP 9, 11, ?, 15, 17? (a) 13 (b) 14 (c) 15 (d) 12
  35. 35.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  36. 36.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 44 (b) 46 (c) 45 (d) 54
  37. 37.What is the 10th term of the AP 19, 27, 35, 43, …? (a) 80 (b) 99 (c) 91 (d) 72
  38. 38.What is the 26th term of the AP 2, 8, 14, 20, …? (a) 158 (b) 156 (c) 150 (d) 152
  39. 39.Which term of the AP 6, 8, 10, 12, … is 56? (a) 27th (b) 28th (c) 26th (d) 25th
  40. 40.What is the 14th term of the AP 7, 12, 17, 22, …? (a) 70 (b) 77 (c) 72 (d) 65

Answer key

  1. 903
  2. 64
  3. 124
  4. 30th
  5. 435
  6. 19
  7. 210
  8. 57
  9. 11th
  10. 3081
  11. 105
  12. 20
  13. 99
  14. 232
  15. 91
  16. 50
  17. 12th
  18. 156
  19. 39
  20. 36th
  21. 15th
  22. 290
  23. 81
  24. 406
  25. 60
  26. 361
  27. 173
  28. 69
  29. 209
  30. 10
  31. 32nd
  32. 45
  33. 95
  34. 13
  35. 25
  36. 45
  37. 91
  38. 152
  39. 26th
  40. 72

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