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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 582 · 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 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 110 (c) 120 (d) 20
  2. 2.What is the 10th term of the AP 10, 17, 24, 31, …? (a) 80 (b) 70 (c) 63 (d) 73
  3. 3.What is the 15th term of the AP 3, 7, 11, 15, …? (a) 60 (b) 56 (c) 59 (d) 63
  4. 4.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 276 (d) 552
  5. 5.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 936 (b) 504 (c) 72 (d) 468
  6. 6.Which term of the AP 16, 19, 22, 25, … is 58? (a) 16th (b) 15th (c) 14th (d) 17th
  7. 7.What is the 15th term of the AP 2, 5, 8, 11, …? (a) 42 (b) 47 (c) 45 (d) 44
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  9. 9.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 52 (b) 104 (c) 56 (d) 10
  10. 10.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 288 (b) 261 (c) 522 (d) 53
  11. 11.What is the 39th term of the AP 15, 24, 33, 42, …? (a) 366 (b) 342 (c) 351 (d) 357
  12. 12.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 204 (b) 408 (c) 224 (d) 43
  13. 13.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 11 (b) 16 (c) 12 (d) 10
  14. 14.What is the 10th term of the AP 13, 15, 17, 19, …? (a) 20 (b) 33 (c) 18 (d) 31
  15. 15.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 11 (b) 10 (c) 8 (d) 9
  16. 16.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 396 (b) 198 (c) 201 (d) 33
  17. 17.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 3081 (c) 6320 (d) 3161
  18. 18.What is the 22nd term of the AP 7, 16, 25, 34, …? (a) 198 (b) 205 (c) 196 (d) 189
  19. 19.What is the 18th term of the AP 7, 12, 17, 22, …? (a) 85 (b) 97 (c) 90 (d) 92
  20. 20.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 26 (b) 28 (c) 34 (d) 27
  21. 21.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 154 (d) 136
  22. 22.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 26 (b) 33 (c) 27 (d) 28
  23. 23.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 496 (c) 497 (d) 992
  24. 24.What is the 19th term of the AP 15, 17, 19, 21, …? (a) 53 (b) 51 (c) 36 (d) 38
  25. 25.What is the 29th term of the AP 20, 24, 28, 32, …? (a) 112 (b) 116 (c) 132 (d) 136
  26. 26.What is the 36th term of the AP 16, 20, 24, 28, …? (a) 140 (b) 160 (c) 144 (d) 156
  27. 27.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  28. 28.Which term of the AP 5, 11, 17, 23, … is 71? (a) 13th (b) 11th (c) 12th (d) 14th
  29. 29.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 12 (b) 16 (c) 10 (d) 11
  30. 30.What is the 13th term of the AP 5, 10, 15, 20, …? (a) 66 (b) 70 (c) 60 (d) 65
  31. 31.What is the 15th term of the AP 9, 15, 21, 27, …? (a) 90 (b) 99 (c) 93 (d) 84
  32. 32.What is the 22nd term of the AP 1, 5, 9, 13, …? (a) 89 (b) 84 (c) 88 (d) 85
  33. 33.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 150 (c) 75 (d) 12
  34. 34.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 65 (b) 450 (c) 900 (d) 480
  35. 35.What is the 13th term of the AP 6, 12, 18, 24, …? (a) 72 (b) 78 (c) 84 (d) 79
  36. 36.Which term of the AP 12, 16, 20, 24, … is 124? (a) 31st (b) 28th (c) 30th (d) 29th
  37. 37.What is the 28th term of the AP 16, 23, 30, 37, …? (a) 189 (b) 212 (c) 196 (d) 205
  38. 38.Which term of the AP 1, 9, 17, 25, … is 217? (a) 27th (b) 30th (c) 29th (d) 28th
  39. 39.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5000 (c) 4950 (d) 5050
  40. 40.What is the 19th term of the AP 7, 14, 21, 28, …? (a) 133 (b) 126 (c) 140 (d) 134

Answer key

  1. 110
  2. 73
  3. 59
  4. 529
  5. 468
  6. 15th
  7. 44
  8. 900
  9. 52
  10. 261
  11. 357
  12. 204
  13. 11
  14. 31
  15. 9
  16. 198
  17. 3160
  18. 196
  19. 92
  20. 27
  21. 153
  22. 27
  23. 496
  24. 51
  25. 132
  26. 156
  27. 169
  28. 12th
  29. 11
  30. 65
  31. 93
  32. 85
  33. 75
  34. 450
  35. 78
  36. 29th
  37. 205
  38. 28th
  39. 5050
  40. 133

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