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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 20 · 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 all the whole numbers from 1 to 14? (a) 98 (b) 91 (c) 210 (d) 105
  2. 2.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 24 (b) 168 (c) 312 (d) 156
  3. 3.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 21 (b) 19 (c) 24 (d) 20
  4. 4.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 153 (c) 171 (d) 162
  5. 5.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 552 (c) 277 (d) 276
  6. 6.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
  7. 7.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4465 (c) 4560 (d) 4561
  8. 8.What is the 16th term of the AP 2, 6, 10, 14, …? (a) 62 (b) 64 (c) 60 (d) 66
  9. 9.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 9702 (c) 4753 (d) 4851
  10. 10.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 552 (b) 1032 (c) 76 (d) 516
  11. 11.Which term of the AP 7, 12, 17, 22, … is 57? (a) 13th (b) 12th (c) 11th (d) 10th
  12. 12.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 33 (b) 153 (c) 306 (d) 171
  13. 13.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 41 (b) 33 (c) 34 (d) 32
  14. 14.Which term of the AP 18, 27, 36, 45, … is 153? (a) 17th (b) 15th (c) 16th (d) 18th
  15. 15.Which term of the AP 10, 13, 16, 19, … is 67? (a) 21st (b) 22nd (c) 19th (d) 20th
  16. 16.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 168 (b) 189 (c) 42 (d) 336
  17. 17.Which term of the AP 2, 5, 8, 11, … is 101? (a) 36th (b) 34th (c) 33rd (d) 35th
  18. 18.Which term of the AP 6, 9, 12, 15, … is 27? (a) 7th (b) 9th (c) 8th (d) 10th
  19. 19.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 22 (b) 264 (c) 143 (d) 132
  20. 20.What is the 24th term of the AP 1, 9, 17, 25, …? (a) 184 (b) 192 (c) 193 (d) 185
  21. 21.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 406 (c) 378 (d) 392
  22. 22.Which term of the AP 1, 10, 19, 28, … is 82? (a) 10th (b) 12th (c) 11th (d) 9th
  23. 23.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 3322 (c) 6642 (d) 3240
  24. 24.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 110 (b) 31 (c) 190 (d) 95
  25. 25.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 19 (b) 14 (c) 15 (d) 16
  26. 26.What is the 12th term of the AP 13, 17, 21, 25, …? (a) 48 (b) 57 (c) 44 (d) 61
  27. 27.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1540 (c) 1541 (d) 3080
  28. 28.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 24 (b) 25 (c) 26 (d) 34
  29. 29.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 78 (b) 132 (c) 66 (d) 21
  30. 30.Which term of the AP 20, 22, 24, 26, … is 48? (a) 16th (b) 14th (c) 24th (d) 15th
  31. 31.What is the 18th term of the AP 2, 11, 20, 29, …? (a) 155 (b) 162 (c) 164 (d) 153
  32. 32.What is the sum of all the whole numbers from 1 to 21? (a) 462 (b) 210 (c) 232 (d) 231
  33. 33.What is the 37th term of the AP 14, 18, 22, 26, …? (a) 162 (b) 148 (c) 144 (d) 158
  34. 34.What is the 12th term of the AP 4, 7, 10, 13, …? (a) 40 (b) 37 (c) 33 (d) 36
  35. 35.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 625 (d) 650
  36. 36.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 60 (b) 35 (c) 30 (d) 10
  37. 37.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 14 (b) 13 (c) 19 (d) 15
  38. 38.Which term of the AP 19, 28, 37, 46, … is 118? (a) 12th (b) 13th (c) 14th (d) 11th
  39. 39.What is the 13th term of the AP 7, 9, 11, 13, …? (a) 33 (b) 31 (c) 24 (d) 26
  40. 40.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 232 (b) 416 (c) 208 (d) 47

Answer key

  1. 105
  2. 156
  3. 20
  4. 171
  5. 276
  6. 729
  7. 4560
  8. 62
  9. 4851
  10. 516
  11. 11th
  12. 153
  13. 33
  14. 16th
  15. 20th
  16. 168
  17. 34th
  18. 8th
  19. 132
  20. 185
  21. 406
  22. 10th
  23. 3321
  24. 95
  25. 15
  26. 57
  27. 1540
  28. 25
  29. 66
  30. 15th
  31. 155
  32. 231
  33. 158
  34. 37
  35. 625
  36. 30
  37. 14
  38. 12th
  39. 31
  40. 208

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