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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 331 · 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 5 terms of the AP 1, 4, 7, …? (a) 35 (b) 38 (c) 70 (d) 13
  2. 2.What is the 35th term of the AP 8, 14, 20, 26, …? (a) 204 (b) 210 (c) 212 (d) 218
  3. 3.What is the 11th term of the AP 13, 16, 19, 22, …? (a) 33 (b) 30 (c) 46 (d) 43
  4. 4.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 49 (d) 325
  5. 5.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  6. 6.Which term of the AP 4, 7, 10, 13, … is 79? (a) 25th (b) 27th (c) 28th (d) 26th
  7. 7.Which term of the AP 12, 14, 16, 18, … is 38? (a) 13th (b) 19th (c) 14th (d) 15th
  8. 8.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 6 (b) 42 (c) 24 (d) 21
  9. 9.What is the 25th term of the AP 7, 9, 11, 13, …? (a) 48 (b) 55 (c) 50 (d) 57
  10. 10.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 8 (b) 9 (c) 13 (d) 10
  11. 11.Which term of the AP 18, 26, 34, 42, … is 266? (a) 32nd (b) 31st (c) 33rd (d) 34th
  12. 12.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 540 (b) 39 (c) 270 (d) 288
  13. 13.Which term of the AP 10, 12, 14, 16, … is 40? (a) 15th (b) 17th (c) 20th (d) 16th
  14. 14.Which term of the AP 18, 21, 24, 27, … is 54? (a) 12th (b) 18th (c) 14th (d) 13th
  15. 15.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 34 (b) 26 (c) 25 (d) 27
  16. 16.What is the 21st term of the AP 9, 13, 17, 21, …? (a) 80 (b) 89 (c) 84 (d) 93
  17. 17.What is the 30th term of the AP 16, 24, 32, 40, …? (a) 240 (b) 232 (c) 256 (d) 248
  18. 18.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 9 (b) 12 (c) 10 (d) 8
  19. 19.What is the 25th term of the AP 6, 15, 24, 33, …? (a) 216 (b) 231 (c) 225 (d) 222
  20. 20.What is the 18th term of the AP 16, 20, 24, 28, …? (a) 88 (b) 68 (c) 72 (d) 84
  21. 21.What is the 37th term of the AP 3, 10, 17, 24, …? (a) 255 (b) 252 (c) 262 (d) 259
  22. 22.What is the missing term in the AP 12, 20, 28, ?, 44? (a) 37 (b) 35 (c) 36 (d) 44
  23. 23.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 9 (b) 42 (c) 78 (d) 39
  24. 24.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 26 (b) 90 (c) 100 (d) 180
  25. 25.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 60 (b) 35 (c) 10 (d) 30
  26. 26.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 33 (d) 153
  27. 27.Which term of the AP 19, 27, 35, 43, … is 163? (a) 18th (b) 20th (c) 19th (d) 21st
  28. 28.Which term of the AP 3, 8, 13, 18, … is 103? (a) 22nd (b) 23rd (c) 20th (d) 21st
  29. 29.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 49 (b) 450 (c) 225 (d) 252
  30. 30.Which term of the AP 8, 11, 14, 17, … is 65? (a) 22nd (b) 21st (c) 20th (d) 19th
  31. 31.Which term of the AP 5, 9, 13, 17, … is 65? (a) 15th (b) 18th (c) 17th (d) 16th
  32. 32.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 243 (b) 225 (c) 450 (d) 41
  33. 33.What is the 26th term of the AP 19, 24, 29, 34, …? (a) 149 (b) 125 (c) 144 (d) 130
  34. 34.What is the 28th term of the AP 7, 12, 17, 22, …? (a) 142 (b) 140 (c) 147 (d) 135
  35. 35.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3362 (c) 3321 (d) 6806
  36. 36.Which term of the AP 7, 9, 11, 13, … is 77? (a) 38th (b) 35th (c) 36th (d) 37th
  37. 37.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 780 (d) 781
  38. 38.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 15 (b) 90 (c) 45 (d) 48
  39. 39.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 128 (c) 136 (d) 272
  40. 40.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 876 (b) 64 (c) 438 (d) 468

Answer key

  1. 35
  2. 212
  3. 43
  4. 625
  5. 900
  6. 26th
  7. 14th
  8. 21
  9. 55
  10. 9
  11. 32nd
  12. 270
  13. 16th
  14. 13th
  15. 26
  16. 89
  17. 248
  18. 9
  19. 222
  20. 84
  21. 255
  22. 36
  23. 39
  24. 90
  25. 30
  26. 289
  27. 19th
  28. 21st
  29. 225
  30. 20th
  31. 16th
  32. 225
  33. 144
  34. 142
  35. 3403
  36. 36th
  37. 780
  38. 45
  39. 136
  40. 438

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