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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 461 · 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 12 terms of the AP 1, 2, 3, …? (a) 156 (b) 12 (c) 78 (d) 84
  2. 2.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 20 (b) 22 (c) 26 (d) 21
  3. 3.What is the 25th term of the AP 20, 26, 32, 38, …? (a) 170 (b) 144 (c) 150 (d) 164
  4. 4.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 11 (b) 17 (c) 13 (d) 12
  5. 5.Which term of the AP 12, 19, 26, 33, … is 271? (a) 38th (b) 40th (c) 37th (d) 39th
  6. 6.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 361 (d) 37
  7. 7.What is the 26th term of the AP 17, 23, 29, 35, …? (a) 150 (b) 173 (c) 156 (d) 167
  8. 8.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 100 (b) 198 (c) 99 (d) 15
  9. 9.What is the 13th term of the AP 4, 7, 10, 13, …? (a) 40 (b) 39 (c) 43 (d) 36
  10. 10.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 50 (b) 41 (c) 43 (d) 42
  11. 11.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 77 (b) 78 (c) 154 (d) 12
  12. 12.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 50 (b) 13 (c) 45 (d) 90
  13. 13.What is the 38th term of the AP 2, 8, 14, 20, …? (a) 228 (b) 222 (c) 224 (d) 230
  14. 14.What is the 15th term of the AP 1, 8, 15, 22, …? (a) 106 (b) 98 (c) 105 (d) 99
  15. 15.What is the 15th term of the AP 7, 13, 19, 25, …? (a) 91 (b) 90 (c) 84 (d) 97
  16. 16.What is the 14th term of the AP 9, 12, 15, 18, …? (a) 51 (b) 39 (c) 48 (d) 42
  17. 17.What is the 11th term of the AP 16, 18, 20, 22, …? (a) 36 (b) 38 (c) 20 (d) 22
  18. 18.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 484 (d) 43
  19. 19.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 310 (b) 170 (c) 29 (d) 155
  20. 20.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 703 (c) 704 (d) 1406
  21. 21.What is the sum of all the whole numbers from 1 to 83? (a) 3486 (b) 6972 (c) 3487 (d) 3403
  22. 22.What is the 26th term of the AP 2, 8, 14, 20, …? (a) 150 (b) 156 (c) 158 (d) 152
  23. 23.What is the 18th term of the AP 8, 17, 26, 35, …? (a) 153 (b) 170 (c) 161 (d) 162
  24. 24.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3322 (c) 3321 (d) 6642
  25. 25.What is the 23rd term of the AP 4, 13, 22, 31, …? (a) 211 (b) 202 (c) 207 (d) 198
  26. 26.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 16 (b) 17 (c) 18 (d) 20
  27. 27.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 10100 (d) 5000
  28. 28.What is the 14th term of the AP 2, 9, 16, 23, …? (a) 98 (b) 100 (c) 91 (d) 93
  29. 29.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 24 (b) 20 (c) 21 (d) 19
  30. 30.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 65 (b) 21 (c) 75 (d) 130
  31. 31.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 936 (b) 504 (c) 468 (d) 72
  32. 32.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 33 (d) 289
  33. 33.What is the 11th term of the AP 3, 6, 9, 12, …? (a) 33 (b) 34 (c) 30 (d) 36
  34. 34.What is the sum of all the whole numbers from 1 to 73? (a) 5402 (b) 2628 (c) 2701 (d) 2702
  35. 35.What is the 33rd term of the AP 8, 10, 12, 14, …? (a) 64 (b) 74 (c) 72 (d) 66
  36. 36.What is the 29th term of the AP 10, 16, 22, 28, …? (a) 178 (b) 174 (c) 168 (d) 184
  37. 37.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 8190 (c) 4095 (d) 4005
  38. 38.Which term of the AP 18, 24, 30, 36, … is 96? (a) 16th (b) 14th (c) 15th (d) 13th
  39. 39.Which term of the AP 9, 17, 25, 33, … is 313? (a) 41st (b) 39th (c) 40th (d) 38th
  40. 40.What is the 29th term of the AP 18, 26, 34, 42, …? (a) 250 (b) 224 (c) 232 (d) 242

Answer key

  1. 78
  2. 21
  3. 164
  4. 12
  5. 38th
  6. 361
  7. 167
  8. 99
  9. 40
  10. 42
  11. 77
  12. 45
  13. 224
  14. 99
  15. 91
  16. 48
  17. 36
  18. 484
  19. 155
  20. 703
  21. 3486
  22. 152
  23. 161
  24. 3321
  25. 202
  26. 17
  27. 5050
  28. 93
  29. 20
  30. 65
  31. 468
  32. 289
  33. 33
  34. 2701
  35. 72
  36. 178
  37. 4095
  38. 14th
  39. 39th
  40. 242

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