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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 547 · 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 16th term of the AP 6, 12, 18, 24, …? (a) 102 (b) 97 (c) 96 (d) 90
  2. 2.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 35 (c) 11 (d) 70
  3. 3.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 42 (b) 9 (c) 39 (d) 78
  4. 4.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4851 (c) 9702 (d) 4753
  5. 5.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 378 (b) 41 (c) 189 (d) 194
  6. 6.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 49 (d) 13
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 45 (d) 90
  8. 8.What is the missing term in the AP 5, 10, ?, 20, 25? (a) 15 (b) 14 (c) 20 (d) 16
  9. 9.What is the 20th term of the AP 12, 14, 16, 18, …? (a) 50 (b) 40 (c) 52 (d) 38
  10. 10.Which term of the AP 8, 17, 26, 35, … is 179? (a) 19th (b) 21st (c) 22nd (d) 20th
  11. 11.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 95 (b) 80 (c) 28 (d) 160
  12. 12.What is the missing term in the AP 16, 22, ?, 34, 40? (a) 27 (b) 29 (c) 34 (d) 28
  13. 13.What is the 34th term of the AP 17, 25, 33, 41, …? (a) 289 (b) 272 (c) 264 (d) 281
  14. 14.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 70 (c) 8 (d) 35
  15. 15.What is the 31st term of the AP 10, 17, 24, 31, …? (a) 220 (b) 217 (c) 227 (d) 210
  16. 16.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
  17. 17.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 196 (b) 175 (c) 350 (d) 43
  18. 18.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 13 (b) 14 (c) 16 (d) 12
  19. 19.Which term of the AP 6, 12, 18, 24, … is 78? (a) 15th (b) 13th (c) 12th (d) 14th
  20. 20.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 20 (b) 21 (c) 29 (d) 22
  21. 21.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 171 (c) 162 (d) 342
  22. 22.Which term of the AP 11, 15, 19, 23, … is 99? (a) 22nd (b) 24th (c) 25th (d) 23rd
  23. 23.What is the missing term in the AP 16, 18, 20, ?, 24? (a) 22 (b) 23 (c) 21 (d) 24
  24. 24.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 35 (b) 36 (c) 43 (d) 34
  25. 25.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 91 (c) 98 (d) 210
  26. 26.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4560 (c) 4656 (d) 4608
  27. 27.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 684 (b) 342 (c) 56 (d) 372
  28. 28.What is the 12th term of the AP 19, 26, 33, 40, …? (a) 84 (b) 77 (c) 96 (d) 103
  29. 29.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 702 (d) 676
  30. 30.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 462 (c) 232 (d) 210
  31. 31.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 160 (b) 144 (c) 288 (d) 32
  32. 32.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 132 (b) 228 (c) 34 (d) 114
  33. 33.What is the 32nd term of the AP 8, 16, 24, 32, …? (a) 256 (b) 257 (c) 264 (d) 248
  34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  35. 35.What is the sum of all the whole numbers from 1 to 74? (a) 5550 (b) 2738 (c) 2701 (d) 2775
  36. 36.What is the 33rd term of the AP 9, 18, 27, 36, …? (a) 306 (b) 297 (c) 298 (d) 288
  37. 37.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 72 (c) 11 (d) 36
  38. 38.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 29 (b) 209 (c) 418 (d) 220
  39. 39.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  40. 40.What is the 20th term of the AP 13, 22, 31, 40, …? (a) 184 (b) 180 (c) 171 (d) 193

Answer key

  1. 96
  2. 35
  3. 39
  4. 4851
  5. 189
  6. 49
  7. 81
  8. 15
  9. 50
  10. 20th
  11. 80
  12. 28
  13. 281
  14. 35
  15. 220
  16. 324
  17. 175
  18. 13
  19. 13th
  20. 21
  21. 171
  22. 23rd
  23. 22
  24. 35
  25. 105
  26. 4656
  27. 342
  28. 96
  29. 676
  30. 231
  31. 144
  32. 114
  33. 256
  34. 900
  35. 2775
  36. 297
  37. 36
  38. 209
  39. 100
  40. 184

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