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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 884 · 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 20th term of the AP 16, 21, 26, 31, …? (a) 111 (b) 116 (c) 95 (d) 100
  2. 2.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 861 (c) 1806 (d) 903
  3. 3.What is the missing term in the AP 20, 23, 26, ?, 32? (a) 28 (b) 29 (c) 32 (d) 30
  4. 4.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 35 (d) 171
  5. 5.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 25 (b) 24 (c) 29 (d) 23
  6. 6.Which term of the AP 11, 13, 15, 17, … is 55? (a) 24th (b) 22nd (c) 23rd (d) 25th
  7. 7.What is the 10th term of the AP 16, 19, 22, 25, …? (a) 43 (b) 30 (c) 27 (d) 46
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  9. 9.What is the 12th term of the AP 7, 16, 25, 34, …? (a) 99 (b) 106 (c) 108 (d) 115
  10. 10.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 784 (d) 812
  11. 11.Which term of the AP 8, 12, 16, 20, … is 72? (a) 17th (b) 16th (c) 18th (d) 19th
  12. 12.Which term of the AP 8, 15, 22, 29, … is 176? (a) 24th (b) 26th (c) 27th (d) 25th
  13. 13.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 105 (d) 196
  14. 14.Which term of the AP 4, 10, 16, 22, … is 46? (a) 7th (b) 9th (c) 8th (d) 10th
  15. 15.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  16. 16.What is the 34th term of the AP 17, 24, 31, 38, …? (a) 255 (b) 238 (c) 248 (d) 231
  17. 17.What is the 40th term of the AP 15, 21, 27, 33, …? (a) 255 (b) 240 (c) 234 (d) 249
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  19. 19.What is the 13th term of the AP 6, 9, 12, 15, …? (a) 39 (b) 36 (c) 42 (d) 45
  20. 20.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4418 (c) 4371 (d) 8930
  21. 21.What is the missing term in the AP 15, 20, ?, 30, 35? (a) 30 (b) 24 (c) 25 (d) 26
  22. 22.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 40 (b) 30 (c) 31 (d) 32
  23. 23.What is the 20th term of the AP 2, 8, 14, 20, …? (a) 120 (b) 116 (c) 114 (d) 122
  24. 24.What is the 25th term of the AP 4, 11, 18, 25, …? (a) 168 (b) 172 (c) 179 (d) 175
  25. 25.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 25 (c) 9 (d) 30
  26. 26.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 2450 (c) 1226 (d) 1176
  27. 27.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 91 (c) 105 (d) 210
  28. 28.What is the 39th term of the AP 5, 12, 19, 26, …? (a) 271 (b) 278 (c) 266 (d) 273
  29. 29.Which term of the AP 8, 17, 26, 35, … is 215? (a) 25th (b) 26th (c) 23rd (d) 24th
  30. 30.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 220 (b) 29 (c) 209 (d) 418
  31. 31.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 191 (c) 380 (d) 190
  32. 32.Which term of the AP 1, 5, 9, 13, … is 117? (a) 31st (b) 29th (c) 30th (d) 32nd
  33. 33.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 10100 (c) 4950 (d) 5000
  34. 34.What is the 34th term of the AP 6, 14, 22, 30, …? (a) 278 (b) 272 (c) 270 (d) 264
  35. 35.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 42 (d) 11
  36. 36.What is the 16th term of the AP 11, 13, 15, 17, …? (a) 32 (b) 41 (c) 30 (d) 43
  37. 37.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 272 (c) 136 (d) 120
  38. 38.What is the 12th term of the AP 4, 12, 20, 28, …? (a) 88 (b) 96 (c) 92 (d) 100
  39. 39.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 36 (b) 40 (c) 8 (d) 72
  40. 40.Which term of the AP 9, 11, 13, 15, … is 69? (a) 33rd (b) 32nd (c) 30th (d) 31st

Answer key

  1. 111
  2. 903
  3. 29
  4. 324
  5. 24
  6. 23rd
  7. 43
  8. 676
  9. 106
  10. 784
  11. 17th
  12. 25th
  13. 196
  14. 8th
  15. 256
  16. 248
  17. 249
  18. 81
  19. 42
  20. 4465
  21. 25
  22. 31
  23. 116
  24. 172
  25. 25
  26. 1225
  27. 105
  28. 271
  29. 24th
  30. 209
  31. 190
  32. 30th
  33. 5050
  34. 270
  35. 36
  36. 41
  37. 136
  38. 92
  39. 36
  40. 31st

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