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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 115 · 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 15th term of the AP 11, 16, 21, 26, …? (a) 86 (b) 70 (c) 75 (d) 81
  2. 2.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 25 (b) 20 (c) 22 (d) 21
  3. 3.What is the 13th term of the AP 17, 22, 27, 32, …? (a) 60 (b) 65 (c) 82 (d) 77
  4. 4.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 756 (d) 378
  5. 5.What is the 19th term of the AP 9, 16, 23, 30, …? (a) 142 (b) 126 (c) 135 (d) 133
  6. 6.What is the 20th term of the AP 14, 22, 30, 38, …? (a) 160 (b) 152 (c) 166 (d) 174
  7. 7.What is the missing term in the AP 8, 16, 24, ?, 40? (a) 31 (b) 32 (c) 40 (d) 33
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 100 (d) 19
  9. 9.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 14 (b) 16 (c) 12 (d) 13
  10. 10.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 5 (b) 4 (c) 9 (d) 6
  11. 11.Which term of the AP 11, 20, 29, 38, … is 353? (a) 39th (b) 41st (c) 38th (d) 40th
  12. 12.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
  13. 13.What is the 39th term of the AP 5, 11, 17, 23, …? (a) 234 (b) 228 (c) 233 (d) 239
  14. 14.What is the 39th term of the AP 5, 14, 23, 32, …? (a) 356 (b) 342 (c) 351 (d) 347
  15. 15.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 50 (c) 26 (d) 25
  16. 16.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 300 (b) 50 (c) 275 (d) 550
  17. 17.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 17 (b) 11 (c) 12 (d) 13
  18. 18.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 11 (c) 40 (d) 35
  19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484
  20. 20.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 28 (b) 37 (c) 30 (d) 29
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 169 (d) 182
  22. 22.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3321 (c) 6642 (d) 3322
  23. 23.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 7656 (c) 3828 (d) 3741
  24. 24.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 136 (d) 256
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 625 (d) 650
  26. 26.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 210 (b) 25 (c) 105 (d) 114
  27. 27.What is the 33rd term of the AP 11, 15, 19, 23, …? (a) 132 (b) 139 (c) 128 (d) 143
  28. 28.Which term of the AP 15, 21, 27, 33, … is 213? (a) 35th (b) 34th (c) 36th (d) 33rd
  29. 29.Which term of the AP 2, 8, 14, 20, … is 206? (a) 37th (b) 36th (c) 35th (d) 34th
  30. 30.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 360 (b) 198 (c) 180 (d) 36
  31. 31.Which term of the AP 16, 18, 20, 22, … is 50? (a) 17th (b) 25th (c) 19th (d) 18th
  32. 32.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 55 (b) 310 (c) 280 (d) 560
  33. 33.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 15 (b) 18 (c) 14 (d) 16
  34. 34.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 11 (d) 42
  35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 171 (d) 342
  36. 36.What is the 18th term of the AP 12, 16, 20, 24, …? (a) 80 (b) 72 (c) 84 (d) 68
  37. 37.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 25 (b) 160 (c) 320 (d) 170
  38. 38.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 17 (d) 81
  39. 39.What is the 25th term of the AP 17, 24, 31, 38, …? (a) 175 (b) 168 (c) 185 (d) 192
  40. 40.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 90 (c) 17 (d) 45

Answer key

  1. 81
  2. 21
  3. 77
  4. 378
  5. 135
  6. 166
  7. 32
  8. 100
  9. 13
  10. 5
  11. 39th
  12. 441
  13. 233
  14. 347
  15. 25
  16. 275
  17. 12
  18. 35
  19. 484
  20. 29
  21. 169
  22. 3321
  23. 3828
  24. 256
  25. 625
  26. 105
  27. 139
  28. 34th
  29. 35th
  30. 180
  31. 18th
  32. 280
  33. 15
  34. 36
  35. 324
  36. 80
  37. 160
  38. 81
  39. 185
  40. 45

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