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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 860 · 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 36th term of the AP 6, 8, 10, 12, …? (a) 78 (b) 70 (c) 76 (d) 72
  2. 2.What is the 10th term of the AP 20, 27, 34, 41, …? (a) 70 (b) 63 (c) 90 (d) 83
  3. 3.What is the 10th term of the AP 3, 11, 19, 27, …? (a) 75 (b) 72 (c) 80 (d) 83
  4. 4.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 6 (b) 4 (c) 5 (d) 9
  5. 5.Which term of the AP 18, 23, 28, 33, … is 53? (a) 7th (b) 9th (c) 10th (d) 8th
  6. 6.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 120 (b) 64 (c) 11 (d) 60
  7. 7.What is the 37th term of the AP 20, 23, 26, 29, …? (a) 108 (b) 111 (c) 131 (d) 128
  8. 8.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 277 (c) 552 (d) 276
  9. 9.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 110 (b) 120 (c) 220 (d) 20
  10. 10.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 3486 (c) 3487 (d) 6972
  11. 11.What is the missing term in the AP 17, 24, 31, ?, 45? (a) 37 (b) 45 (c) 38 (d) 39
  12. 12.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 1260 (c) 595 (d) 630
  13. 13.Which term of the AP 7, 12, 17, 22, … is 162? (a) 33rd (b) 31st (c) 34th (d) 32nd
  14. 14.What is the 31st term of the AP 12, 17, 22, 27, …? (a) 150 (b) 167 (c) 155 (d) 162
  15. 15.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 190 (c) 37 (d) 361
  16. 16.Which term of the AP 6, 9, 12, 15, … is 75? (a) 25th (b) 23rd (c) 26th (d) 24th
  17. 17.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 150 (b) 23 (c) 75 (d) 85
  18. 18.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 27 (b) 192 (c) 204 (d) 384
  19. 19.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  20. 20.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 288 (b) 144 (c) 39 (d) 162
  21. 21.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 4561 (c) 9120 (d) 4560
  22. 22.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 30 (b) 40 (c) 32 (d) 31
  23. 23.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 46 (b) 37 (c) 39 (d) 38
  24. 24.Which term of the AP 9, 13, 17, 21, … is 93? (a) 22nd (b) 24th (c) 23rd (d) 21st
  25. 25.What is the missing term in the AP 13, 21, 29, ?, 45? (a) 38 (b) 36 (c) 45 (d) 37
  26. 26.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 126 (b) 72 (c) 63 (d) 18
  27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  28. 28.What is the 36th term of the AP 3, 12, 21, 30, …? (a) 315 (b) 318 (c) 324 (d) 327
  29. 29.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 28 (b) 93 (c) 108 (d) 186
  30. 30.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 492 (b) 74 (c) 984 (d) 528
  31. 31.What is the 32nd term of the AP 13, 21, 29, 37, …? (a) 248 (b) 269 (c) 256 (d) 261
  32. 32.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 29 (b) 28 (c) 30 (d) 37
  33. 33.Which term of the AP 3, 5, 7, 9, … is 25? (a) 13th (b) 11th (c) 14th (d) 12th
  34. 34.Which term of the AP 3, 7, 11, 15, … is 155? (a) 41st (b) 38th (c) 39th (d) 40th
  35. 35.Which term of the AP 20, 24, 28, 32, … is 176? (a) 39th (b) 44th (c) 41st (d) 40th
  36. 36.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 15 (b) 16 (c) 17 (d) 21
  37. 37.Which term of the AP 16, 22, 28, 34, … is 100? (a) 16th (b) 17th (c) 14th (d) 15th
  38. 38.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 170 (b) 13 (c) 90 (d) 85
  39. 39.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 204 (b) 27 (c) 114 (d) 102
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 19 (d) 55

Answer key

  1. 76
  2. 83
  3. 75
  4. 5
  5. 8th
  6. 60
  7. 128
  8. 276
  9. 110
  10. 3486
  11. 38
  12. 630
  13. 32nd
  14. 162
  15. 361
  16. 24th
  17. 75
  18. 192
  19. 441
  20. 144
  21. 4560
  22. 31
  23. 38
  24. 22nd
  25. 37
  26. 63
  27. 64
  28. 318
  29. 93
  30. 492
  31. 261
  32. 29
  33. 12th
  34. 39th
  35. 40th
  36. 16
  37. 15th
  38. 85
  39. 102
  40. 100

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