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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 932 · 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 12 terms of the AP 8, 10, 12, …? (a) 228 (b) 30 (c) 240 (d) 456
  2. 2.Which term of the AP 13, 17, 21, 25, … is 65? (a) 14th (b) 15th (c) 13th (d) 16th
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 11 (d) 36
  4. 4.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 248 (b) 124 (c) 136 (d) 26
  5. 5.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 17 (b) 80 (c) 88 (d) 160
  6. 6.What is the 35th term of the AP 1, 4, 7, 10, …? (a) 102 (b) 103 (c) 106 (d) 105
  7. 7.What is the sum of all the whole numbers from 1 to 89? (a) 4005 (b) 3916 (c) 4006 (d) 8010
  8. 8.What is the missing term in the AP 17, 21, 25, ?, 33? (a) 28 (b) 33 (c) 30 (d) 29
  9. 9.Which term of the AP 15, 18, 21, 24, … is 87? (a) 26th (b) 29th (c) 24th (d) 25th
  10. 10.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 56 (b) 13 (c) 49 (d) 98
  11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 276 (d) 529
  12. 12.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 210 (b) 105 (c) 30 (d) 120
  13. 13.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 75 (b) 21 (c) 65 (d) 130
  14. 14.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 1190 (c) 595 (d) 561
  15. 15.What is the 16th term of the AP 5, 11, 17, 23, …? (a) 96 (b) 101 (c) 95 (d) 90
  16. 16.Which term of the AP 13, 18, 23, 28, … is 83? (a) 14th (b) 15th (c) 16th (d) 17th
  17. 17.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 49 (d) 650
  18. 18.What is the 14th term of the AP 6, 10, 14, 18, …? (a) 62 (b) 56 (c) 58 (d) 52
  19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 153 (d) 306
  20. 20.What is the 28th term of the AP 7, 9, 11, 13, …? (a) 56 (b) 54 (c) 63 (d) 61
  21. 21.Which term of the AP 18, 22, 26, 30, … is 142? (a) 33rd (b) 31st (c) 34th (d) 32nd
  22. 22.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 45 (b) 216 (c) 192 (d) 384
  23. 23.What is the 37th term of the AP 10, 19, 28, 37, …? (a) 324 (b) 343 (c) 334 (d) 333
  24. 24.What is the 30th term of the AP 19, 22, 25, 28, …? (a) 90 (b) 106 (c) 109 (d) 87
  25. 25.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 10 (c) 30 (d) 60
  26. 26.What is the 10th term of the AP 4, 10, 16, 22, …? (a) 60 (b) 64 (c) 58 (d) 54
  27. 27.Which term of the AP 4, 10, 16, 22, … is 100? (a) 19th (b) 16th (c) 17th (d) 18th
  28. 28.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 272 (b) 496 (c) 52 (d) 248
  29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  30. 30.Which term of the AP 1, 5, 9, 13, … is 61? (a) 15th (b) 18th (c) 16th (d) 17th
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  32. 32.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 820 (c) 780 (d) 800
  33. 33.What is the 38th term of the AP 12, 20, 28, 36, …? (a) 304 (b) 296 (c) 316 (d) 308
  34. 34.What is the 20th term of the AP 15, 24, 33, 42, …? (a) 171 (b) 186 (c) 180 (d) 195
  35. 35.What is the 20th term of the AP 3, 8, 13, 18, …? (a) 98 (b) 95 (c) 100 (d) 103
  36. 36.What is the 36th term of the AP 4, 9, 14, 19, …? (a) 175 (b) 179 (c) 180 (d) 184
  37. 37.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 18 (b) 300 (c) 156 (d) 150
  38. 38.What is the 28th term of the AP 5, 7, 9, 11, …? (a) 61 (b) 56 (c) 59 (d) 54
  39. 39.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
  40. 40.What is the 39th term of the AP 14, 18, 22, 26, …? (a) 152 (b) 166 (c) 170 (d) 156

Answer key

  1. 228
  2. 14th
  3. 36
  4. 124
  5. 80
  6. 103
  7. 4005
  8. 29
  9. 25th
  10. 49
  11. 529
  12. 105
  13. 65
  14. 595
  15. 95
  16. 15th
  17. 625
  18. 58
  19. 289
  20. 61
  21. 32nd
  22. 192
  23. 334
  24. 106
  25. 30
  26. 58
  27. 17th
  28. 248
  29. 100
  30. 16th
  31. 121
  32. 820
  33. 308
  34. 186
  35. 98
  36. 179
  37. 150
  38. 59
  39. 729
  40. 166

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