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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 961 · 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.Which term of the AP 6, 10, 14, 18, … is 90? (a) 24th (b) 21st (c) 23rd (d) 22nd
  2. 2.What is the 15th term of the AP 16, 21, 26, 31, …? (a) 86 (b) 91 (c) 75 (d) 70
  3. 3.What is the 12th term of the AP 19, 21, 23, 25, …? (a) 22 (b) 43 (c) 24 (d) 41
  4. 4.What is the 24th term of the AP 10, 13, 16, 19, …? (a) 82 (b) 69 (c) 72 (d) 79
  5. 5.Which term of the AP 4, 9, 14, 19, … is 139? (a) 30th (b) 27th (c) 28th (d) 29th
  6. 6.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 558 (b) 306 (c) 279 (d) 55
  7. 7.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 576 (d) 300
  8. 8.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1431 (c) 2970 (d) 1485
  9. 9.Which term of the AP 6, 8, 10, 12, … is 64? (a) 29th (b) 32nd (c) 31st (d) 30th
  10. 10.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 384 (b) 38 (c) 208 (d) 192
  11. 11.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 324 (d) 35
  12. 12.What is the 33rd term of the AP 16, 22, 28, 34, …? (a) 208 (b) 192 (c) 214 (d) 198
  13. 13.What is the 23rd term of the AP 4, 9, 14, 19, …? (a) 119 (b) 114 (c) 115 (d) 110
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 21 (d) 66
  15. 15.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 676 (d) 702
  16. 16.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 2926 (c) 3003 (d) 3004
  17. 17.Which term of the AP 12, 18, 24, 30, … is 144? (a) 25th (b) 22nd (c) 24th (d) 23rd
  18. 18.What is the 11th term of the AP 13, 22, 31, 40, …? (a) 103 (b) 99 (c) 90 (d) 112
  19. 19.What is the 31st term of the AP 8, 12, 16, 20, …? (a) 120 (b) 132 (c) 128 (d) 124
  20. 20.Which term of the AP 9, 15, 21, 27, … is 123? (a) 20th (b) 19th (c) 21st (d) 22nd
  21. 21.What is the 22nd term of the AP 20, 28, 36, 44, …? (a) 196 (b) 188 (c) 168 (d) 176
  22. 22.What is the 20th term of the AP 17, 21, 25, 29, …? (a) 97 (b) 76 (c) 80 (d) 93
  23. 23.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 18 (b) 84 (c) 78 (d) 156
  24. 24.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  25. 25.What is the 15th term of the AP 2, 7, 12, 17, …? (a) 72 (b) 75 (c) 77 (d) 70
  26. 26.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 174 (b) 87 (c) 22 (d) 96
  27. 27.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 26 (b) 25 (c) 24 (d) 32
  28. 28.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 276 (d) 45
  29. 29.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 41 (d) 231
  30. 30.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 4187 (c) 4186 (d) 8372
  31. 31.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 37 (b) 266 (c) 154 (d) 133
  32. 32.What is the 17th term of the AP 12, 20, 28, 36, …? (a) 128 (b) 136 (c) 148 (d) 140
  33. 33.Which term of the AP 7, 13, 19, 25, … is 241? (a) 42nd (b) 40th (c) 41st (d) 39th
  34. 34.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 160 (b) 148 (c) 296 (d) 29
  35. 35.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 21 (b) 87 (c) 84 (d) 168
  36. 36.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 1332 (c) 630 (d) 648
  37. 37.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 21 (b) 15 (c) 16 (d) 17
  38. 38.Which term of the AP 7, 13, 19, 25, … is 133? (a) 24th (b) 23rd (c) 22nd (d) 21st
  39. 39.What is the 15th term of the AP 3, 9, 15, 21, …? (a) 90 (b) 93 (c) 87 (d) 84
  40. 40.What is the 40th term of the AP 2, 5, 8, 11, …? (a) 117 (b) 122 (c) 119 (d) 120

Answer key

  1. 22nd
  2. 86
  3. 41
  4. 79
  5. 28th
  6. 279
  7. 576
  8. 1485
  9. 30th
  10. 192
  11. 324
  12. 208
  13. 114
  14. 121
  15. 676
  16. 3003
  17. 23rd
  18. 103
  19. 128
  20. 20th
  21. 188
  22. 93
  23. 78
  24. 144
  25. 72
  26. 87
  27. 25
  28. 529
  29. 441
  30. 4186
  31. 133
  32. 140
  33. 40th
  34. 148
  35. 84
  36. 666
  37. 16
  38. 22nd
  39. 87
  40. 119

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