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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 960 · 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 10, 12, 14, …? (a) 200 (b) 380 (c) 190 (d) 28
  2. 2.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 81 (b) 89 (c) 78 (d) 92
  3. 3.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 15 (b) 13 (c) 14 (d) 22
  4. 4.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 792 (b) 429 (c) 66 (d) 396
  5. 5.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 117 (b) 234 (c) 118 (d) 17
  6. 6.Which term of the AP 6, 13, 20, 27, … is 195? (a) 27th (b) 29th (c) 28th (d) 30th
  7. 7.What is the 27th term of the AP 7, 13, 19, 25, …? (a) 163 (b) 156 (c) 169 (d) 162
  8. 8.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 154 (c) 136 (d) 153
  9. 9.What is the 25th term of the AP 5, 8, 11, 14, …? (a) 77 (b) 72 (c) 80 (d) 75
  10. 10.What is the sum of all the whole numbers from 1 to 55? (a) 3080 (b) 1541 (c) 1540 (d) 1485
  11. 11.What is the 13th term of the AP 7, 10, 13, 16, …? (a) 43 (b) 46 (c) 39 (d) 36
  12. 12.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2592 (c) 2628 (d) 5256
  13. 13.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 947 (c) 903 (d) 1892
  14. 14.What is the 17th term of the AP 3, 12, 21, 30, …? (a) 144 (b) 153 (c) 147 (d) 156
  15. 15.What is the 35th term of the AP 10, 14, 18, 22, …? (a) 140 (b) 146 (c) 150 (d) 136
  16. 16.What is the 16th term of the AP 15, 19, 23, 27, …? (a) 75 (b) 64 (c) 60 (d) 79
  17. 17.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 406 (d) 55
  18. 18.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 741 (c) 1560 (d) 781
  19. 19.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  20. 20.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 340 (b) 61 (c) 370 (d) 680
  21. 21.What is the 16th term of the AP 18, 26, 34, 42, …? (a) 120 (b) 138 (c) 128 (d) 146
  22. 22.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 91 (b) 180 (c) 14 (d) 90
  23. 23.Which term of the AP 2, 10, 18, 26, … is 202? (a) 27th (b) 28th (c) 25th (d) 26th
  24. 24.What is the 13th term of the AP 12, 18, 24, 30, …? (a) 84 (b) 72 (c) 78 (d) 90
  25. 25.What is the missing term in the AP 3, 11, 19, ?, 35? (a) 27 (b) 35 (c) 28 (d) 26
  26. 26.What is the 37th term of the AP 12, 15, 18, 21, …? (a) 120 (b) 123 (c) 108 (d) 111
  27. 27.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3042 (d) 3081
  28. 28.What is the 25th term of the AP 6, 11, 16, 21, …? (a) 125 (b) 120 (c) 126 (d) 131
  29. 29.What is the 16th term of the AP 6, 8, 10, 12, …? (a) 38 (b) 32 (c) 30 (d) 36
  30. 30.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1485 (c) 2970 (d) 1458
  31. 31.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 407 (b) 64 (c) 748 (d) 374
  32. 32.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 77 (b) 16 (c) 70 (d) 140
  33. 33.What is the 27th term of the AP 14, 21, 28, 35, …? (a) 182 (b) 196 (c) 189 (d) 203
  34. 34.Which term of the AP 11, 16, 21, 26, … is 156? (a) 31st (b) 30th (c) 32nd (d) 29th
  35. 35.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 13 (b) 11 (c) 14 (d) 12
  36. 36.Which term of the AP 10, 19, 28, 37, … is 289? (a) 32nd (b) 31st (c) 33rd (d) 34th
  37. 37.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 140 (b) 35 (c) 145 (d) 280
  38. 38.Which term of the AP 3, 10, 17, 24, … is 178? (a) 27th (b) 26th (c) 28th (d) 25th
  39. 39.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 110 (d) 100
  40. 40.What is the 29th term of the AP 14, 16, 18, 20, …? (a) 56 (b) 70 (c) 72 (d) 58

Answer key

  1. 190
  2. 89
  3. 14
  4. 396
  5. 117
  6. 28th
  7. 163
  8. 153
  9. 77
  10. 1540
  11. 43
  12. 2628
  13. 946
  14. 147
  15. 146
  16. 75
  17. 784
  18. 780
  19. 49
  20. 340
  21. 138
  22. 90
  23. 26th
  24. 84
  25. 27
  26. 120
  27. 3081
  28. 126
  29. 36
  30. 1485
  31. 374
  32. 70
  33. 196
  34. 30th
  35. 12
  36. 32nd
  37. 140
  38. 26th
  39. 100
  40. 70

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