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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 991 · 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, 8, 14, …? (a) 56 (b) 290 (c) 320 (d) 580
  2. 2.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 21 (b) 18 (c) 19 (d) 20
  3. 3.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 1682 (c) 3422 (d) 1711
  4. 4.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 33 (d) 153
  5. 5.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 96 (c) 15 (d) 92
  6. 6.Which term of the AP 5, 10, 15, 20, … is 40? (a) 7th (b) 9th (c) 10th (d) 8th
  7. 7.Which term of the AP 1, 3, 5, 7, … is 53? (a) 29th (b) 28th (c) 27th (d) 26th
  8. 8.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 272 (c) 128 (d) 120
  9. 9.What is the 31st term of the AP 17, 22, 27, 32, …? (a) 167 (b) 150 (c) 155 (d) 172
  10. 10.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 444 (b) 480 (c) 888 (d) 70
  11. 11.Which term of the AP 4, 12, 20, 28, … is 132? (a) 17th (b) 18th (c) 19th (d) 16th
  12. 12.What is the 12th term of the AP 7, 16, 25, 34, …? (a) 99 (b) 106 (c) 115 (d) 108
  13. 13.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 9 (b) 11 (c) 17 (d) 10
  14. 14.What is the 35th term of the AP 20, 29, 38, 47, …? (a) 326 (b) 335 (c) 315 (d) 306
  15. 15.What is the 20th term of the AP 19, 28, 37, 46, …? (a) 199 (b) 171 (c) 180 (d) 190
  16. 16.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 22 (b) 92 (c) 104 (d) 184
  17. 17.Which term of the AP 18, 25, 32, 39, … is 102? (a) 15th (b) 12th (c) 14th (d) 13th
  18. 18.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 396 (b) 209 (c) 198 (d) 28
  19. 19.What is the 40th term of the AP 14, 18, 22, 26, …? (a) 160 (b) 156 (c) 174 (d) 170
  20. 20.What is the 16th term of the AP 14, 23, 32, 41, …? (a) 149 (b) 135 (c) 144 (d) 158
  21. 21.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 35 (d) 70
  22. 22.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 520 (b) 260 (c) 44 (d) 280
  23. 23.What is the 16th term of the AP 15, 18, 21, 24, …? (a) 63 (b) 45 (c) 60 (d) 48
  24. 24.Which term of the AP 1, 10, 19, 28, … is 271? (a) 30th (b) 32nd (c) 33rd (d) 31st
  25. 25.What is the 28th term of the AP 1, 3, 5, 7, …? (a) 57 (b) 56 (c) 54 (d) 55
  26. 26.What is the 13th term of the AP 4, 8, 12, 16, …? (a) 53 (b) 48 (c) 52 (d) 56
  27. 27.What is the 20th term of the AP 12, 14, 16, 18, …? (a) 52 (b) 38 (c) 50 (d) 40
  28. 28.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 4802 (c) 9702 (d) 4851
  29. 29.What is the 28th term of the AP 13, 19, 25, 31, …? (a) 168 (b) 175 (c) 162 (d) 181
  30. 30.Which term of the AP 18, 24, 30, 36, … is 108? (a) 15th (b) 17th (c) 18th (d) 16th
  31. 31.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 350 (b) 55 (c) 325 (d) 650
  32. 32.Which term of the AP 14, 23, 32, 41, … is 113? (a) 12th (b) 11th (c) 14th (d) 13th
  33. 33.What is the 23rd term of the AP 4, 9, 14, 19, …? (a) 119 (b) 115 (c) 114 (d) 110
  34. 34.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 2775 (c) 2701 (d) 5550
  35. 35.What is the missing term in the AP 8, 11, ?, 17, 20? (a) 14 (b) 17 (c) 13 (d) 15
  36. 36.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 120 (b) 32 (c) 102 (d) 204
  37. 37.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 576 (d) 300
  38. 38.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 7656 (c) 3828 (d) 3741
  39. 39.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3741 (c) 7482 (d) 3655
  40. 40.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 48 (b) 84 (c) 42 (d) 12

Answer key

  1. 290
  2. 19
  3. 1711
  4. 289
  5. 92
  6. 8th
  7. 27th
  8. 136
  9. 167
  10. 444
  11. 17th
  12. 106
  13. 10
  14. 326
  15. 190
  16. 92
  17. 13th
  18. 198
  19. 170
  20. 149
  21. 35
  22. 260
  23. 60
  24. 31st
  25. 55
  26. 52
  27. 50
  28. 4851
  29. 175
  30. 16th
  31. 325
  32. 12th
  33. 114
  34. 2775
  35. 14
  36. 102
  37. 576
  38. 3828
  39. 3741
  40. 42

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