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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 931 · 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 11 terms of the AP 8, 9, 10, …? (a) 286 (b) 144 (c) 143 (d) 18
  2. 2.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 162 (b) 26 (c) 81 (d) 96
  3. 3.What is the 16th term of the AP 3, 5, 7, 9, …? (a) 32 (b) 33 (c) 30 (d) 35
  4. 4.What is the 40th term of the AP 19, 22, 25, 28, …? (a) 120 (b) 136 (c) 139 (d) 117
  5. 5.What is the 36th term of the AP 10, 19, 28, 37, …? (a) 324 (b) 315 (c) 334 (d) 325
  6. 6.What is the 25th term of the AP 15, 17, 19, 21, …? (a) 65 (b) 50 (c) 48 (d) 63
  7. 7.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 60 (b) 65 (c) 120 (d) 16
  8. 8.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 288 (b) 153 (c) 144 (d) 24
  9. 9.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 112 (b) 200 (c) 100 (d) 23
  10. 10.What is the missing term in the AP 14, ?, 26, 32, 38? (a) 20 (b) 26 (c) 19 (d) 21
  11. 11.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  12. 12.What is the 14th term of the AP 15, 20, 25, 30, …? (a) 80 (b) 65 (c) 70 (d) 85
  13. 13.What is the 18th term of the AP 16, 24, 32, 40, …? (a) 160 (b) 144 (c) 136 (d) 152
  14. 14.What is the 13th term of the AP 10, 12, 14, 16, …? (a) 34 (b) 36 (c) 24 (d) 26
  15. 15.Which term of the AP 4, 10, 16, 22, … is 208? (a) 37th (b) 35th (c) 34th (d) 36th
  16. 16.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 231 (b) 30 (c) 440 (d) 220
  17. 17.What is the missing term in the AP 16, 22, ?, 34, 40? (a) 34 (b) 28 (c) 27 (d) 29
  18. 18.What is the 26th term of the AP 2, 11, 20, 29, …? (a) 225 (b) 236 (c) 227 (d) 234
  19. 19.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 55 (b) 560 (c) 310 (d) 280
  20. 20.Which term of the AP 4, 8, 12, 16, … is 152? (a) 40th (b) 39th (c) 37th (d) 38th
  21. 21.What is the missing term in the AP 15, 22, ?, 36, 43? (a) 30 (b) 28 (c) 36 (d) 29
  22. 22.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3570 (c) 3528 (d) 7140
  23. 23.What is the 11th term of the AP 14, 17, 20, 23, …? (a) 30 (b) 47 (c) 33 (d) 44
  24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  25. 25.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 512 (c) 1056 (d) 528
  26. 26.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 2926 (c) 3003 (d) 6006
  27. 27.What is the sum of all the whole numbers from 1 to 89? (a) 4006 (b) 8010 (c) 4005 (d) 3916
  28. 28.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 127 (b) 18 (c) 126 (d) 252
  29. 29.Which term of the AP 4, 7, 10, 13, … is 31? (a) 11th (b) 12th (c) 10th (d) 9th
  30. 30.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 91 (c) 98 (d) 105
  31. 31.Which term of the AP 17, 22, 27, 32, … is 132? (a) 25th (b) 26th (c) 24th (d) 23rd
  32. 32.What is the 11th term of the AP 2, 4, 6, 8, …? (a) 22 (b) 23 (c) 24 (d) 20
  33. 33.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 19 (b) 90 (c) 168 (d) 84
  34. 34.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 40 (c) 36 (d) 8
  35. 35.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 25 (d) 30
  36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 841 (d) 435
  37. 37.What is the 32nd term of the AP 12, 21, 30, 39, …? (a) 288 (b) 300 (c) 279 (d) 291
  38. 38.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 154 (c) 153 (d) 306
  39. 39.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 252 (b) 26 (c) 126 (d) 129
  40. 40.What is the missing term in the AP 5, ?, 21, 29, 37? (a) 21 (b) 12 (c) 14 (d) 13

Answer key

  1. 143
  2. 81
  3. 33
  4. 136
  5. 325
  6. 63
  7. 60
  8. 144
  9. 100
  10. 20
  11. 64
  12. 80
  13. 152
  14. 34
  15. 35th
  16. 220
  17. 28
  18. 227
  19. 280
  20. 38th
  21. 29
  22. 3570
  23. 44
  24. 81
  25. 528
  26. 3003
  27. 4005
  28. 126
  29. 10th
  30. 105
  31. 24th
  32. 22
  33. 84
  34. 36
  35. 25
  36. 841
  37. 291
  38. 153
  39. 126
  40. 13

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