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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 801 · 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 36? (a) 666 (b) 1332 (c) 630 (d) 648
  2. 2.What is the 37th term of the AP 14, 18, 22, 26, …? (a) 148 (b) 144 (c) 158 (d) 162
  3. 3.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 462 (b) 41 (c) 231 (d) 253
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  5. 5.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 191 (c) 190 (d) 171
  6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  7. 7.What is the 35th term of the AP 1, 5, 9, 13, …? (a) 137 (b) 141 (c) 136 (d) 140
  8. 8.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1432 (c) 1378 (d) 1431
  9. 9.What is the 17th term of the AP 16, 24, 32, 40, …? (a) 136 (b) 152 (c) 128 (d) 144
  10. 10.What is the 16th term of the AP 14, 21, 28, 35, …? (a) 105 (b) 119 (c) 112 (d) 126
  11. 11.What is the 16th term of the AP 3, 11, 19, 27, …? (a) 128 (b) 123 (c) 120 (d) 131
  12. 12.What is the 12th term of the AP 17, 22, 27, 32, …? (a) 77 (b) 60 (c) 55 (d) 72
  13. 13.What is the sum of all the whole numbers from 1 to 87? (a) 7656 (b) 3829 (c) 3828 (d) 3741
  14. 14.What is the 16th term of the AP 15, 20, 25, 30, …? (a) 80 (b) 95 (c) 90 (d) 75
  15. 15.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 24 (b) 16 (c) 18 (d) 17
  16. 16.What is the 30th term of the AP 20, 29, 38, 47, …? (a) 270 (b) 290 (c) 261 (d) 281
  17. 17.What is the missing term in the AP 9, 11, ?, 15, 17? (a) 15 (b) 12 (c) 14 (d) 13
  18. 18.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 15 (b) 168 (c) 84 (d) 85
  19. 19.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 47 (c) 300 (d) 600
  20. 20.What is the 22nd term of the AP 3, 7, 11, 15, …? (a) 87 (b) 91 (c) 84 (d) 88
  21. 21.What is the 11th term of the AP 1, 9, 17, 25, …? (a) 81 (b) 80 (c) 89 (d) 88
  22. 22.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 870 (c) 406 (d) 435
  23. 23.Which term of the AP 4, 7, 10, 13, … is 73? (a) 23rd (b) 26th (c) 24th (d) 25th
  24. 24.Which term of the AP 2, 6, 10, 14, … is 42? (a) 12th (b) 13th (c) 11th (d) 10th
  25. 25.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 39 (c) 400 (d) 210
  26. 26.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 220 (c) 20 (d) 110
  27. 27.What is the 11th term of the AP 11, 13, 15, 17, …? (a) 20 (b) 22 (c) 31 (d) 33
  28. 28.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 105 (d) 196
  29. 29.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 198 (b) 99 (c) 15 (d) 100
  30. 30.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 49 (d) 325
  31. 31.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 27 (b) 198 (c) 374 (d) 187
  32. 32.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 165 (b) 330 (c) 20 (d) 166
  33. 33.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 132 (b) 21 (c) 78 (d) 66
  34. 34.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 22 (b) 252 (c) 126 (d) 135
  35. 35.What is the 28th term of the AP 14, 21, 28, 35, …? (a) 210 (b) 189 (c) 203 (d) 196
  36. 36.Which term of the AP 9, 13, 17, 21, … is 61? (a) 15th (b) 13th (c) 16th (d) 14th
  37. 37.What is the sum of all the whole numbers from 1 to 79? (a) 3081 (b) 3160 (c) 3161 (d) 6320
  38. 38.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 9 (b) 44 (c) 88 (d) 48
  39. 39.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 27 (b) 35 (c) 28 (d) 26
  40. 40.What is the 40th term of the AP 7, 10, 13, 16, …? (a) 127 (b) 120 (c) 117 (d) 124

Answer key

  1. 666
  2. 158
  3. 231
  4. 25
  5. 190
  6. 81
  7. 137
  8. 1431
  9. 144
  10. 119
  11. 123
  12. 72
  13. 3828
  14. 90
  15. 17
  16. 281
  17. 13
  18. 84
  19. 576
  20. 87
  21. 81
  22. 435
  23. 24th
  24. 11th
  25. 400
  26. 110
  27. 31
  28. 196
  29. 99
  30. 625
  31. 187
  32. 165
  33. 66
  34. 126
  35. 203
  36. 14th
  37. 3160
  38. 44
  39. 27
  40. 124

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