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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 657 · 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 24th term of the AP 15, 17, 19, 21, …? (a) 48 (b) 63 (c) 61 (d) 46
  2. 2.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 90 (b) 156 (c) 78 (d) 23
  3. 3.Which term of the AP 1, 3, 5, 7, … is 69? (a) 37th (b) 35th (c) 34th (d) 36th
  4. 4.What is the 37th term of the AP 4, 11, 18, 25, …? (a) 252 (b) 259 (c) 256 (d) 263
  5. 5.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 420 (b) 840 (c) 68 (d) 456
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
  7. 7.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2312 (c) 2278 (d) 2346
  8. 8.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4560 (c) 9312 (d) 4608
  9. 9.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 65 (c) 11 (d) 70
  10. 10.What is the 16th term of the AP 16, 25, 34, 43, …? (a) 160 (b) 144 (c) 151 (d) 135
  11. 11.What is the 27th term of the AP 20, 29, 38, 47, …? (a) 243 (b) 263 (c) 234 (d) 254
  12. 12.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 192 (b) 104 (c) 19 (d) 96
  13. 13.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 14 (c) 102 (d) 108
  14. 14.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 198 (b) 36 (c) 180 (d) 360
  15. 15.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 32 (b) 41 (c) 34 (d) 33
  16. 16.What is the 33rd term of the AP 5, 14, 23, 32, …? (a) 302 (b) 288 (c) 297 (d) 293
  17. 17.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 22 (b) 25 (c) 20 (d) 21
  18. 18.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 456 (b) 492 (c) 912 (d) 71
  19. 19.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 31 (b) 175 (c) 190 (d) 350
  20. 20.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  21. 21.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 25 (b) 24 (c) 23 (d) 33
  22. 22.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4232 (c) 4186 (d) 4278
  23. 23.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 27 (b) 174 (c) 102 (d) 87
  24. 24.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 40 (c) 6 (d) 21
  25. 25.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 23 (b) 19 (c) 20 (d) 18
  26. 26.What is the 10th term of the AP 3, 5, 7, 9, …? (a) 23 (b) 18 (c) 20 (d) 21
  27. 27.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 19 (b) 17 (c) 20 (d) 18
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  29. 29.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 3540 (c) 1770 (d) 1771
  30. 30.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 3321 (c) 6642 (d) 3240
  31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  32. 32.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 2450 (c) 1226 (d) 1176
  33. 33.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 595 (c) 631 (d) 1260
  34. 34.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 396 (b) 34 (c) 198 (d) 201
  35. 35.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 468 (b) 46 (c) 239 (d) 234
  36. 36.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 3 (c) 4 (d) 5
  37. 37.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 220 (b) 125 (c) 34 (d) 110
  38. 38.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2048 (c) 2080 (d) 2016
  39. 39.What is the 36th term of the AP 4, 12, 20, 28, …? (a) 280 (b) 288 (c) 284 (d) 292
  40. 40.What is the 21st term of the AP 2, 11, 20, 29, …? (a) 191 (b) 189 (c) 182 (d) 180

Answer key

  1. 61
  2. 78
  3. 35th
  4. 256
  5. 420
  6. 25
  7. 2346
  8. 4656
  9. 65
  10. 151
  11. 254
  12. 96
  13. 102
  14. 180
  15. 33
  16. 293
  17. 21
  18. 456
  19. 175
  20. 841
  21. 24
  22. 4278
  23. 87
  24. 20
  25. 19
  26. 21
  27. 18
  28. 100
  29. 1770
  30. 3321
  31. 196
  32. 1225
  33. 630
  34. 198
  35. 234
  36. 4
  37. 110
  38. 2080
  39. 284
  40. 182

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