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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 609 · 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 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 105 (d) 210
  2. 2.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 252 (b) 30 (c) 126 (d) 140
  3. 3.What is the missing term in the AP 8, 13, 18, ?, 28? (a) 24 (b) 22 (c) 23 (d) 28
  4. 4.What is the missing term in the AP 5, ?, 21, 29, 37? (a) 13 (b) 12 (c) 14 (d) 21
  5. 5.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 54 (b) 13 (c) 48 (d) 96
  6. 6.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 7 (b) 8 (c) 5 (d) 6
  7. 7.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 1036 (c) 990 (d) 2070
  8. 8.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 490 (b) 270 (c) 47 (d) 245
  9. 9.What is the 40th term of the AP 18, 25, 32, 39, …? (a) 298 (b) 280 (c) 291 (d) 273
  10. 10.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 70 (b) 35 (c) 36 (d) 8
  11. 11.Which term of the AP 14, 18, 22, 26, … is 98? (a) 22nd (b) 21st (c) 23rd (d) 24th
  12. 12.What is the missing term in the AP 5, 14, ?, 32, 41? (a) 24 (b) 22 (c) 23 (d) 32
  13. 13.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 441 (d) 462
  14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 289 (d) 33
  15. 15.Which term of the AP 6, 9, 12, 15, … is 63? (a) 20th (b) 19th (c) 21st (d) 22nd
  16. 16.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 9 (c) 30 (d) 15
  17. 17.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 6162 (c) 3003 (d) 3042
  18. 18.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 272 (b) 152 (c) 136 (d) 31
  19. 19.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2080 (c) 2146 (d) 2145
  20. 20.What is the 17th term of the AP 1, 4, 7, 10, …? (a) 51 (b) 52 (c) 49 (d) 48
  21. 21.What is the 21st term of the AP 15, 23, 31, 39, …? (a) 183 (b) 168 (c) 175 (d) 160
  22. 22.What is the 20th term of the AP 6, 13, 20, 27, …? (a) 133 (b) 140 (c) 139 (d) 146
  23. 23.What is the 34th term of the AP 5, 14, 23, 32, …? (a) 311 (b) 306 (c) 297 (d) 302
  24. 24.Which term of the AP 4, 11, 18, 25, … is 123? (a) 18th (b) 20th (c) 19th (d) 17th
  25. 25.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 800 (c) 820 (d) 1640
  26. 26.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 55 (d) 19
  27. 27.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 136 (b) 120 (c) 240 (d) 29
  28. 28.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 374 (b) 59 (c) 379 (d) 748
  29. 29.Which term of the AP 3, 6, 9, 12, … is 30? (a) 11th (b) 9th (c) 10th (d) 12th
  30. 30.What is the 19th term of the AP 7, 9, 11, 13, …? (a) 38 (b) 45 (c) 43 (d) 36
  31. 31.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 27 (b) 29 (c) 28 (d) 36
  32. 32.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2278 (c) 4556 (d) 2279
  33. 33.Which term of the AP 14, 21, 28, 35, … is 168? (a) 23rd (b) 25th (c) 22nd (d) 24th
  34. 34.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 99 (b) 198 (c) 108 (d) 24
  35. 35.What is the 27th term of the AP 7, 9, 11, 13, …? (a) 54 (b) 52 (c) 59 (d) 61
  36. 36.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 10 (b) 9 (c) 15 (d) 11
  37. 37.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 812 (c) 55 (d) 406
  38. 38.What is the 25th term of the AP 1, 5, 9, 13, …? (a) 101 (b) 100 (c) 97 (d) 96
  39. 39.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4608 (c) 9312 (d) 4560
  40. 40.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 78 (c) 91 (d) 182

Answer key

  1. 196
  2. 126
  3. 23
  4. 13
  5. 48
  6. 6
  7. 1035
  8. 245
  9. 291
  10. 35
  11. 22nd
  12. 23
  13. 441
  14. 289
  15. 20th
  16. 25
  17. 3081
  18. 136
  19. 2145
  20. 49
  21. 175
  22. 139
  23. 302
  24. 18th
  25. 820
  26. 100
  27. 120
  28. 374
  29. 10th
  30. 43
  31. 28
  32. 2278
  33. 23rd
  34. 99
  35. 59
  36. 10
  37. 784
  38. 97
  39. 4656
  40. 91

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