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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 261 · 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 terms of the AP 6, 8, 10, …? (a) 72 (b) 16 (c) 66 (d) 132
  2. 2.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 29 (b) 28 (c) 30 (d) 35
  3. 3.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 852 (b) 426 (c) 63 (d) 456
  4. 4.What is the 39th term of the AP 4, 6, 8, 10, …? (a) 82 (b) 76 (c) 80 (d) 78
  5. 5.What is the missing term in the AP 20, 28, 36, ?, 52? (a) 52 (b) 44 (c) 43 (d) 45
  6. 6.What is the 20th term of the AP 6, 13, 20, 27, …? (a) 140 (b) 133 (c) 139 (d) 146
  7. 7.What is the 28th term of the AP 20, 25, 30, 35, …? (a) 155 (b) 140 (c) 160 (d) 135
  8. 8.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 33 (b) 210 (c) 195 (d) 390
  9. 9.What is the 17th term of the AP 16, 19, 22, 25, …? (a) 51 (b) 64 (c) 67 (d) 48
  10. 10.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 486 (b) 51 (c) 243 (d) 270
  11. 11.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 22 (b) 84 (c) 72 (d) 144
  12. 12.What is the 11th term of the AP 10, 15, 20, 25, …? (a) 50 (b) 60 (c) 55 (d) 65
  13. 13.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 54 (b) 768 (c) 384 (d) 408
  14. 14.Which term of the AP 5, 14, 23, 32, … is 302? (a) 34th (b) 35th (c) 36th (d) 33rd
  15. 15.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 15 (b) 13 (c) 14 (d) 17
  16. 16.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 153 (d) 289
  17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 15 (d) 25
  18. 18.What is the 40th term of the AP 11, 16, 21, 26, …? (a) 206 (b) 195 (c) 200 (d) 211
  19. 19.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1953 (c) 1891 (d) 3906
  20. 20.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 616 (b) 308 (c) 48 (d) 330
  21. 21.What is the 21st term of the AP 4, 8, 12, 16, …? (a) 80 (b) 85 (c) 84 (d) 88
  22. 22.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 22 (b) 24 (c) 25 (d) 23
  23. 23.What is the 36th term of the AP 13, 15, 17, 19, …? (a) 70 (b) 83 (c) 72 (d) 85
  24. 24.What is the 20th term of the AP 2, 4, 6, 8, …? (a) 41 (b) 40 (c) 42 (d) 38
  25. 25.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 52 (b) 297 (c) 594 (d) 302
  26. 26.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 29 (b) 100 (c) 190 (d) 95
  27. 27.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 348 (b) 20 (c) 180 (d) 174
  28. 28.What is the missing term in the AP 16, 23, 30, ?, 44? (a) 44 (b) 37 (c) 36 (d) 38
  29. 29.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 4465 (c) 4560 (d) 9120
  30. 30.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 4371 (c) 8742 (d) 4278
  31. 31.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 210 (d) 39
  32. 32.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 49 (d) 625
  33. 33.What is the 13th term of the AP 16, 21, 26, 31, …? (a) 65 (b) 81 (c) 60 (d) 76
  34. 34.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 130 (b) 65 (c) 80 (d) 25
  35. 35.Which term of the AP 1, 6, 11, 16, … is 116? (a) 24th (b) 23rd (c) 26th (d) 25th
  36. 36.What is the 38th term of the AP 17, 25, 33, 41, …? (a) 304 (b) 313 (c) 321 (d) 296
  37. 37.What is the 12th term of the AP 3, 5, 7, 9, …? (a) 25 (b) 24 (c) 27 (d) 22
  38. 38.What is the 26th term of the AP 9, 18, 27, 36, …? (a) 234 (b) 225 (c) 243 (d) 235
  39. 39.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  40. 40.Which term of the AP 10, 15, 20, 25, … is 55? (a) 11th (b) 9th (c) 12th (d) 10th

Answer key

  1. 66
  2. 29
  3. 426
  4. 80
  5. 44
  6. 139
  7. 155
  8. 195
  9. 64
  10. 243
  11. 72
  12. 60
  13. 384
  14. 34th
  15. 14
  16. 289
  17. 25
  18. 206
  19. 1953
  20. 308
  21. 84
  22. 23
  23. 83
  24. 40
  25. 297
  26. 95
  27. 174
  28. 37
  29. 4560
  30. 4371
  31. 400
  32. 625
  33. 76
  34. 65
  35. 24th
  36. 313
  37. 25
  38. 234
  39. 49
  40. 10th

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