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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 130 · 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 5 terms of the AP 8, 13, 18, …? (a) 90 (b) 180 (c) 95 (d) 28
  2. 2.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 196 (b) 350 (c) 175 (d) 43
  3. 3.Which term of the AP 15, 19, 23, 27, … is 135? (a) 30th (b) 32nd (c) 33rd (d) 31st
  4. 4.What is the 19th term of the AP 10, 15, 20, 25, …? (a) 90 (b) 105 (c) 95 (d) 100
  5. 5.What is the 12th term of the AP 12, 15, 18, 21, …? (a) 33 (b) 36 (c) 48 (d) 45
  6. 6.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 25 (b) 20 (c) 18 (d) 19
  7. 7.What is the 34th term of the AP 16, 18, 20, 22, …? (a) 84 (b) 82 (c) 66 (d) 68
  8. 8.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 166 (b) 330 (c) 20 (d) 165
  9. 9.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 5700 (c) 2850 (d) 2775
  10. 10.What is the 13th term of the AP 16, 25, 34, 43, …? (a) 124 (b) 133 (c) 117 (d) 108
  11. 11.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 580 (b) 290 (c) 320 (d) 56
  12. 12.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 946 (c) 947 (d) 903
  13. 13.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 360 (b) 26 (c) 180 (d) 192
  14. 14.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 344 (b) 39 (c) 172 (d) 192
  15. 15.What is the 15th term of the AP 14, 20, 26, 32, …? (a) 98 (b) 104 (c) 90 (d) 84
  16. 16.What is the 25th term of the AP 10, 16, 22, 28, …? (a) 150 (b) 154 (c) 160 (d) 144
  17. 17.Which term of the AP 19, 28, 37, 46, … is 208? (a) 21st (b) 22nd (c) 24th (d) 23rd
  18. 18.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 200 (b) 38 (c) 400 (d) 220
  19. 19.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 224 (b) 115 (c) 25 (d) 112
  20. 20.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 51 (b) 285 (c) 310 (d) 570
  21. 21.Which term of the AP 20, 22, 24, 26, … is 96? (a) 48th (b) 40th (c) 39th (d) 38th
  22. 22.Which term of the AP 17, 21, 25, 29, … is 57? (a) 11th (b) 13th (c) 12th (d) 10th
  23. 23.What is the missing term in the AP 9, 11, ?, 15, 17? (a) 15 (b) 14 (c) 12 (d) 13
  24. 24.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 108 (b) 17 (c) 112 (d) 216
  25. 25.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 702 (d) 351
  26. 26.What is the 19th term of the AP 3, 11, 19, 27, …? (a) 147 (b) 144 (c) 152 (d) 155
  27. 27.What is the 37th term of the AP 20, 23, 26, 29, …? (a) 131 (b) 111 (c) 128 (d) 108
  28. 28.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 29 (b) 27 (c) 35 (d) 28
  29. 29.What is the 18th term of the AP 16, 24, 32, 40, …? (a) 152 (b) 144 (c) 136 (d) 160
  30. 30.What is the 11th term of the AP 12, 18, 24, 30, …? (a) 78 (b) 72 (c) 66 (d) 60
  31. 31.What is the 18th term of the AP 11, 17, 23, 29, …? (a) 108 (b) 119 (c) 113 (d) 102
  32. 32.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 90 (b) 168 (c) 84 (d) 19
  33. 33.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 112 (b) 120 (c) 21 (d) 224
  34. 34.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 156 (b) 78 (c) 18 (d) 84
  35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 45 (d) 276
  36. 36.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 3240 (c) 3160 (d) 6480
  37. 37.What is the 16th term of the AP 17, 20, 23, 26, …? (a) 45 (b) 48 (c) 65 (d) 62
  38. 38.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 304 (b) 33 (c) 168 (d) 152
  39. 39.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 78 (c) 156 (d) 23
  40. 40.What is the 10th term of the AP 15, 19, 23, 27, …? (a) 51 (b) 40 (c) 36 (d) 55

Answer key

  1. 90
  2. 175
  3. 31st
  4. 100
  5. 45
  6. 19
  7. 82
  8. 165
  9. 2850
  10. 124
  11. 290
  12. 946
  13. 180
  14. 172
  15. 98
  16. 154
  17. 22nd
  18. 200
  19. 112
  20. 285
  21. 39th
  22. 11th
  23. 13
  24. 108
  25. 351
  26. 147
  27. 128
  28. 28
  29. 152
  30. 72
  31. 113
  32. 84
  33. 112
  34. 78
  35. 529
  36. 3240
  37. 62
  38. 152
  39. 144
  40. 51

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