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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 879 · 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 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  2. 2.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 172 (b) 39 (c) 344 (d) 192
  3. 3.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 33 (b) 294 (c) 147 (d) 161
  4. 4.What is the 21st term of the AP 20, 22, 24, 26, …? (a) 62 (b) 40 (c) 60 (d) 42
  5. 5.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 7482 (c) 3698 (d) 3741
  6. 6.What is the missing term in the AP 16, 20, 24, ?, 32? (a) 28 (b) 29 (c) 27 (d) 32
  7. 7.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 230 (b) 120 (c) 16 (d) 115
  8. 8.Which term of the AP 18, 21, 24, 27, … is 90? (a) 30th (b) 24th (c) 26th (d) 25th
  9. 9.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 722 (c) 703 (d) 1482
  10. 10.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 27 (b) 28 (c) 34 (d) 26
  11. 11.What is the 11th term of the AP 18, 23, 28, 33, …? (a) 68 (b) 50 (c) 73 (d) 55
  12. 12.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 22 (b) 21 (c) 26 (d) 23
  13. 13.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 465 (c) 497 (d) 496
  14. 14.What is the 11th term of the AP 15, 19, 23, 27, …? (a) 59 (b) 40 (c) 55 (d) 44
  15. 15.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 110 (b) 55 (c) 13 (d) 56
  16. 16.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 340 (b) 620 (c) 58 (d) 310
  17. 17.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 21 (b) 23 (c) 30 (d) 22
  18. 18.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4186 (c) 4187 (d) 4095
  19. 19.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 270 (b) 138 (c) 135 (d) 27
  20. 20.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 92 (b) 81 (c) 78 (d) 89
  21. 21.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3403 (c) 6806 (d) 3321
  22. 22.What is the 11th term of the AP 18, 27, 36, 45, …? (a) 117 (b) 90 (c) 108 (d) 99
  23. 23.Which term of the AP 12, 21, 30, 39, … is 147? (a) 15th (b) 17th (c) 18th (d) 16th
  24. 24.What is the missing term in the AP 8, ?, 26, 35, 44? (a) 17 (b) 26 (c) 16 (d) 18
  25. 25.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1432 (c) 1431 (d) 1378
  26. 26.What is the 13th term of the AP 8, 12, 16, 20, …? (a) 52 (b) 48 (c) 60 (d) 56
  27. 27.What is the 33rd term of the AP 5, 12, 19, 26, …? (a) 224 (b) 229 (c) 236 (d) 231
  28. 28.What is the 34th term of the AP 3, 5, 7, 9, …? (a) 69 (b) 68 (c) 71 (d) 66
  29. 29.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 180 (b) 330 (c) 30 (d) 165
  30. 30.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 10 (b) 52 (c) 56 (d) 104
  31. 31.What is the 25th term of the AP 5, 10, 15, 20, …? (a) 120 (b) 125 (c) 126 (d) 130
  32. 32.Which term of the AP 20, 22, 24, 26, … is 68? (a) 34th (b) 24th (c) 26th (d) 25th
  33. 33.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 63 (b) 72 (c) 18 (d) 126
  34. 34.Which term of the AP 14, 18, 22, 26, … is 166? (a) 41st (b) 40th (c) 39th (d) 38th
  35. 35.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 102 (b) 51 (c) 54 (d) 11
  36. 36.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 132 (d) 21
  37. 37.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 27 (b) 26 (c) 25 (d) 33
  38. 38.What is the 11th term of the AP 5, 14, 23, 32, …? (a) 104 (b) 95 (c) 90 (d) 99
  39. 39.What is the missing term in the AP 14, ?, 26, 32, 38? (a) 20 (b) 21 (c) 26 (d) 19
  40. 40.What is the 20th term of the AP 7, 9, 11, 13, …? (a) 38 (b) 47 (c) 45 (d) 40

Answer key

  1. 81
  2. 172
  3. 147
  4. 60
  5. 3741
  6. 28
  7. 115
  8. 25th
  9. 741
  10. 27
  11. 68
  12. 22
  13. 496
  14. 55
  15. 55
  16. 310
  17. 22
  18. 4186
  19. 135
  20. 89
  21. 3403
  22. 108
  23. 16th
  24. 17
  25. 1431
  26. 56
  27. 229
  28. 69
  29. 165
  30. 52
  31. 125
  32. 25th
  33. 63
  34. 39th
  35. 51
  36. 121
  37. 26
  38. 95
  39. 20
  40. 45

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