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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 523 · 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 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
  2. 2.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 13 (b) 12 (c) 17 (d) 11
  3. 3.What is the 25th term of the AP 5, 11, 17, 23, …? (a) 144 (b) 150 (c) 149 (d) 155
  4. 4.What is the 35th term of the AP 9, 17, 25, 33, …? (a) 289 (b) 272 (c) 281 (d) 280
  5. 5.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 160 (b) 95 (c) 28 (d) 80
  6. 6.What is the 38th term of the AP 7, 11, 15, 19, …? (a) 159 (b) 152 (c) 155 (d) 148
  7. 7.What is the 36th term of the AP 13, 21, 29, 37, …? (a) 301 (b) 280 (c) 288 (d) 293
  8. 8.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 276 (d) 552
  9. 9.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 32 (b) 31 (c) 41 (d) 33
  10. 10.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 190 (d) 200
  11. 11.What is the 27th term of the AP 12, 20, 28, 36, …? (a) 208 (b) 228 (c) 216 (d) 220
  12. 12.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 90 (b) 9 (c) 46 (d) 45
  13. 13.What is the 17th term of the AP 5, 14, 23, 32, …? (a) 149 (b) 153 (c) 158 (d) 144
  14. 14.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 186 (c) 93 (d) 28
  15. 15.What is the 27th term of the AP 6, 9, 12, 15, …? (a) 84 (b) 78 (c) 81 (d) 87
  16. 16.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 77 (c) 78 (d) 12
  17. 17.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 10 (b) 8 (c) 15 (d) 9
  18. 18.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 160 (b) 83 (c) 22 (d) 80
  19. 19.Which term of the AP 6, 10, 14, 18, … is 82? (a) 20th (b) 21st (c) 19th (d) 22nd
  20. 20.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 888 (b) 444 (c) 480 (d) 70
  21. 21.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 210 (c) 91 (d) 98
  22. 22.What is the missing term in the AP 8, 15, 22, ?, 36? (a) 29 (b) 30 (c) 36 (d) 28
  23. 23.Which term of the AP 12, 14, 16, 18, … is 38? (a) 15th (b) 14th (c) 13th (d) 19th
  24. 24.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 16 (b) 25 (c) 17 (d) 18
  25. 25.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 17 (b) 144 (c) 72 (d) 78
  26. 26.Which term of the AP 2, 4, 6, 8, … is 34? (a) 16th (b) 19th (c) 17th (d) 18th
  27. 27.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 31 (b) 60 (c) 8 (d) 30
  28. 28.What is the missing term in the AP 16, 20, 24, ?, 32? (a) 32 (b) 27 (c) 28 (d) 29
  29. 29.What is the 26th term of the AP 2, 5, 8, 11, …? (a) 78 (b) 80 (c) 77 (d) 75
  30. 30.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 384 (b) 216 (c) 45 (d) 192
  31. 31.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 174 (b) 180 (c) 348 (d) 20
  32. 32.Which term of the AP 4, 7, 10, 13, … is 55? (a) 17th (b) 20th (c) 18th (d) 19th
  33. 33.What is the 14th term of the AP 17, 23, 29, 35, …? (a) 84 (b) 78 (c) 101 (d) 95
  34. 34.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3322 (c) 3321 (d) 3240
  35. 35.What is the 29th term of the AP 12, 18, 24, 30, …? (a) 174 (b) 180 (c) 186 (d) 168
  36. 36.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 3192 (c) 1540 (d) 1568
  37. 37.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 1250 (c) 2550 (d) 1275
  38. 38.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 8 (b) 13 (c) 10 (d) 9
  39. 39.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 80 (b) 40 (c) 43 (d) 14
  40. 40.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 170 (b) 85 (c) 100 (d) 29

Answer key

  1. 36
  2. 12
  3. 149
  4. 281
  5. 80
  6. 155
  7. 293
  8. 529
  9. 32
  10. 210
  11. 220
  12. 45
  13. 149
  14. 93
  15. 84
  16. 77
  17. 9
  18. 80
  19. 20th
  20. 444
  21. 105
  22. 29
  23. 14th
  24. 17
  25. 72
  26. 17th
  27. 30
  28. 28
  29. 77
  30. 192
  31. 174
  32. 18th
  33. 95
  34. 3321
  35. 180
  36. 1596
  37. 1275
  38. 9
  39. 40
  40. 85

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