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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 855 · 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 48? (a) 1176 (b) 1128 (c) 2352 (d) 1152
  2. 2.What is the 15th term of the AP 4, 11, 18, 25, …? (a) 98 (b) 105 (c) 109 (d) 102
  3. 3.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 52 (b) 496 (c) 272 (d) 248
  4. 4.Which term of the AP 4, 12, 20, 28, … is 140? (a) 18th (b) 19th (c) 20th (d) 17th
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 56 (d) 49
  6. 6.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 374 (b) 27 (c) 187 (d) 198
  7. 7.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 22 (b) 23 (c) 28 (d) 21
  8. 8.What is the 14th term of the AP 13, 15, 17, 19, …? (a) 41 (b) 26 (c) 28 (d) 39
  9. 9.What is the 15th term of the AP 19, 25, 31, 37, …? (a) 84 (b) 109 (c) 90 (d) 103
  10. 10.What is the 31st term of the AP 19, 23, 27, 31, …? (a) 124 (b) 143 (c) 120 (d) 139
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  12. 12.What is the 16th term of the AP 20, 25, 30, 35, …? (a) 100 (b) 95 (c) 75 (d) 80
  13. 13.What is the 15th term of the AP 15, 17, 19, 21, …? (a) 28 (b) 45 (c) 30 (d) 43
  14. 14.What is the 32nd term of the AP 10, 16, 22, 28, …? (a) 192 (b) 186 (c) 196 (d) 202
  15. 15.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 73 (b) 960 (c) 480 (d) 516
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
  17. 17.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 21 (b) 20 (c) 27 (d) 22
  18. 18.Which term of the AP 10, 18, 26, 34, … is 290? (a) 37th (b) 36th (c) 35th (d) 38th
  19. 19.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 28 (b) 30 (c) 38 (d) 29
  20. 20.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 8 (b) 9 (c) 17 (d) 10
  21. 21.Which term of the AP 17, 26, 35, 44, … is 134? (a) 15th (b) 16th (c) 14th (d) 13th
  22. 22.What is the 27th term of the AP 3, 8, 13, 18, …? (a) 135 (b) 133 (c) 130 (d) 138
  23. 23.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 153 (d) 306
  24. 24.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2485 (d) 2450
  25. 25.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 171 (c) 190 (d) 380
  26. 26.What is the 35th term of the AP 5, 9, 13, 17, …? (a) 145 (b) 141 (c) 140 (d) 136
  27. 27.Which term of the AP 17, 24, 31, 38, … is 129? (a) 19th (b) 18th (c) 17th (d) 16th
  28. 28.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 54 (b) 48 (c) 96 (d) 13
  29. 29.What is the 39th term of the AP 19, 23, 27, 31, …? (a) 175 (b) 156 (c) 171 (d) 152
  30. 30.Which term of the AP 18, 23, 28, 33, … is 133? (a) 26th (b) 25th (c) 24th (d) 23rd
  31. 31.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  32. 32.What is the sum of all the whole numbers from 1 to 21? (a) 462 (b) 232 (c) 231 (d) 210
  33. 33.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 22 (b) 21 (c) 23 (d) 24
  34. 34.What is the missing term in the AP 19, 28, 37, ?, 55? (a) 45 (b) 46 (c) 55 (d) 47
  35. 35.What is the 14th term of the AP 5, 7, 9, 11, …? (a) 26 (b) 31 (c) 33 (d) 28
  36. 36.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 60 (b) 15 (c) 110 (d) 55
  37. 37.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 29 (b) 27 (c) 28 (d) 35
  38. 38.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 550 (b) 45 (c) 297 (d) 275
  39. 39.Which term of the AP 4, 12, 20, 28, … is 84? (a) 13th (b) 11th (c) 10th (d) 12th
  40. 40.Which term of the AP 15, 21, 27, 33, … is 135? (a) 23rd (b) 21st (c) 22nd (d) 20th

Answer key

  1. 1176
  2. 102
  3. 248
  4. 18th
  5. 49
  6. 187
  7. 22
  8. 39
  9. 103
  10. 139
  11. 144
  12. 95
  13. 43
  14. 196
  15. 480
  16. 121
  17. 21
  18. 36th
  19. 29
  20. 9
  21. 14th
  22. 133
  23. 289
  24. 2485
  25. 190
  26. 141
  27. 17th
  28. 48
  29. 171
  30. 24th
  31. 441
  32. 231
  33. 22
  34. 46
  35. 31
  36. 55
  37. 28
  38. 275
  39. 11th
  40. 21st

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