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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 448 · 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 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 325 (d) 650
  2. 2.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
  3. 3.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 231 (b) 462 (c) 234 (d) 36
  4. 4.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 56 (b) 682 (c) 346 (d) 341
  5. 5.What is the 35th term of the AP 9, 12, 15, 18, …? (a) 114 (b) 102 (c) 105 (d) 111
  6. 6.What is the sum of all the whole numbers from 1 to 70? (a) 4970 (b) 2485 (c) 2415 (d) 2450
  7. 7.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 43 (b) 40 (c) 80 (d) 14
  8. 8.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 3240 (c) 6642 (d) 3321
  9. 9.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 29 (b) 30 (c) 28 (d) 35
  10. 10.What is the 33rd term of the AP 16, 18, 20, 22, …? (a) 82 (b) 64 (c) 66 (d) 80
  11. 11.What is the 35th term of the AP 12, 15, 18, 21, …? (a) 102 (b) 117 (c) 105 (d) 114
  12. 12.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 180 (b) 40 (c) 360 (d) 200
  13. 13.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 17 (b) 25 (c) 18 (d) 16
  14. 14.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 15 (b) 14 (c) 22 (d) 13
  15. 15.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  16. 16.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  17. 17.What is the missing term in the AP 19, ?, 25, 28, 31? (a) 25 (b) 22 (c) 23 (d) 21
  18. 18.What is the 17th term of the AP 1, 6, 11, 16, …? (a) 86 (b) 81 (c) 85 (d) 80
  19. 19.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 240 (b) 48 (c) 432 (d) 216
  20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  21. 21.What is the 40th term of the AP 12, 14, 16, 18, …? (a) 80 (b) 78 (c) 92 (d) 90
  22. 22.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1378 (c) 1431 (d) 1432
  23. 23.What is the 19th term of the AP 11, 20, 29, 38, …? (a) 171 (b) 162 (c) 182 (d) 173
  24. 24.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 2970 (c) 1458 (d) 1485
  25. 25.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  26. 26.What is the 40th term of the AP 8, 17, 26, 35, …? (a) 368 (b) 359 (c) 360 (d) 351
  27. 27.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 19 (b) 84 (c) 90 (d) 168
  28. 28.What is the 35th term of the AP 2, 7, 12, 17, …? (a) 170 (b) 177 (c) 172 (d) 175
  29. 29.Which term of the AP 16, 22, 28, 34, … is 118? (a) 17th (b) 19th (c) 20th (d) 18th
  30. 30.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 184 (b) 92 (c) 22 (d) 104
  31. 31.What is the 10th term of the AP 7, 15, 23, 31, …? (a) 79 (b) 87 (c) 80 (d) 72
  32. 32.What is the 19th term of the AP 19, 28, 37, 46, …? (a) 171 (b) 181 (c) 190 (d) 162
  33. 33.Which term of the AP 8, 16, 24, 32, … is 192? (a) 23rd (b) 25th (c) 24th (d) 26th
  34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 702 (d) 351
  35. 35.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 210 (d) 400
  36. 36.Which term of the AP 8, 12, 16, 20, … is 136? (a) 33rd (b) 32nd (c) 34th (d) 35th
  37. 37.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 336 (b) 180 (c) 25 (d) 168
  38. 38.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 21 (b) 105 (c) 210 (d) 112
  39. 39.Which term of the AP 12, 21, 30, 39, … is 336? (a) 37th (b) 36th (c) 38th (d) 39th
  40. 40.What is the 19th term of the AP 6, 15, 24, 33, …? (a) 162 (b) 171 (c) 168 (d) 177

Answer key

  1. 625
  2. 121
  3. 231
  4. 341
  5. 111
  6. 2485
  7. 40
  8. 3321
  9. 29
  10. 80
  11. 114
  12. 180
  13. 17
  14. 14
  15. 441
  16. 49
  17. 22
  18. 81
  19. 216
  20. 81
  21. 90
  22. 1431
  23. 173
  24. 1485
  25. 91
  26. 359
  27. 84
  28. 172
  29. 18th
  30. 92
  31. 79
  32. 181
  33. 24th
  34. 676
  35. 400
  36. 33rd
  37. 168
  38. 105
  39. 37th
  40. 168

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