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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 348 · 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 missing term in the AP 5, 10, ?, 20, 25? (a) 15 (b) 20 (c) 14 (d) 16
  2. 2.Which term of the AP 7, 14, 21, 28, … is 238? (a) 34th (b) 36th (c) 33rd (d) 35th
  3. 3.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 3906 (c) 1922 (d) 1953
  4. 4.What is the 38th term of the AP 4, 10, 16, 22, …? (a) 228 (b) 226 (c) 232 (d) 222
  5. 5.What is the missing term in the AP 18, ?, 30, 36, 42? (a) 23 (b) 25 (c) 30 (d) 24
  6. 6.What is the 10th term of the AP 1, 9, 17, 25, …? (a) 81 (b) 80 (c) 73 (d) 72
  7. 7.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 631 (c) 630 (d) 595
  8. 8.What is the sum of all the whole numbers from 1 to 66? (a) 2145 (b) 4422 (c) 2178 (d) 2211
  9. 9.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 11 (c) 36 (d) 42
  10. 10.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 28 (b) 56 (c) 29 (d) 7
  11. 11.What is the 13th term of the AP 4, 11, 18, 25, …? (a) 91 (b) 88 (c) 84 (d) 95
  12. 12.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 100 (b) 26 (c) 90 (d) 180
  13. 13.What is the 26th term of the AP 9, 14, 19, 24, …? (a) 139 (b) 125 (c) 134 (d) 130
  14. 14.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 748 (b) 59 (c) 374 (d) 379
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 55 (d) 110
  16. 16.Which term of the AP 5, 8, 11, 14, … is 50? (a) 16th (b) 18th (c) 15th (d) 17th
  17. 17.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  18. 18.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 4951 (c) 4950 (d) 9900
  19. 19.What is the 33rd term of the AP 8, 13, 18, 23, …? (a) 173 (b) 160 (c) 165 (d) 168
  20. 20.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 34 (b) 396 (c) 198 (d) 201
  21. 21.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1431 (c) 1485 (d) 2970
  22. 22.What is the 12th term of the AP 4, 8, 12, 16, …? (a) 48 (b) 44 (c) 49 (d) 52
  23. 23.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 300 (d) 47
  24. 24.Which term of the AP 10, 13, 16, 19, … is 64? (a) 21st (b) 19th (c) 18th (d) 20th
  25. 25.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 171 (c) 380 (d) 191
  26. 26.Which term of the AP 17, 19, 21, 23, … is 93? (a) 39th (b) 38th (c) 41st (d) 40th
  27. 27.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 12 (b) 72 (c) 73 (d) 144
  28. 28.What is the 23rd term of the AP 4, 10, 16, 22, …? (a) 136 (b) 138 (c) 132 (d) 142
  29. 29.What is the 17th term of the AP 3, 12, 21, 30, …? (a) 144 (b) 156 (c) 153 (d) 147
  30. 30.What is the 35th term of the AP 3, 6, 9, 12, …? (a) 105 (b) 106 (c) 108 (d) 102
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 15 (d) 36
  32. 32.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 19 (b) 150 (c) 145 (d) 290
  33. 33.Which term of the AP 15, 21, 27, 33, … is 141? (a) 22nd (b) 24th (c) 21st (d) 23rd
  34. 34.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 88 (b) 84 (c) 14 (d) 168
  35. 35.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 1035 (c) 2162 (d) 1081
  36. 36.Which term of the AP 11, 15, 19, 23, … is 147? (a) 34th (b) 35th (c) 36th (d) 37th
  37. 37.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4656 (c) 4753 (d) 9506
  38. 38.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 90 (b) 55 (c) 17 (d) 45
  39. 39.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 12 (b) 9 (c) 7 (d) 8
  40. 40.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 17 (b) 19 (c) 25 (d) 18

Answer key

  1. 15
  2. 34th
  3. 1953
  4. 226
  5. 24
  6. 73
  7. 630
  8. 2211
  9. 36
  10. 28
  11. 88
  12. 90
  13. 134
  14. 374
  15. 100
  16. 16th
  17. 441
  18. 4950
  19. 168
  20. 198
  21. 1485
  22. 48
  23. 576
  24. 19th
  25. 190
  26. 39th
  27. 72
  28. 136
  29. 147
  30. 105
  31. 64
  32. 145
  33. 22nd
  34. 84
  35. 1081
  36. 35th
  37. 4753
  38. 45
  39. 8
  40. 18

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