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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 301 · 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 8 terms of the AP 4, 10, 16, …? (a) 46 (b) 224 (c) 400 (d) 200
  2. 2.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  3. 3.What is the 10th term of the AP 8, 14, 20, 26, …? (a) 54 (b) 62 (c) 68 (d) 60
  4. 4.Which term of the AP 12, 15, 18, 21, … is 87? (a) 27th (b) 26th (c) 29th (d) 25th
  5. 5.Which term of the AP 19, 26, 33, 40, … is 110? (a) 15th (b) 16th (c) 13th (d) 14th
  6. 6.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1326 (c) 2756 (d) 1378
  7. 7.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 126 (b) 252 (c) 26 (d) 129
  8. 8.Which term of the AP 14, 23, 32, 41, … is 77? (a) 9th (b) 10th (c) 7th (d) 8th
  9. 9.Which term of the AP 19, 21, 23, 25, … is 69? (a) 26th (b) 25th (c) 27th (d) 28th
  10. 10.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 14 (b) 20 (c) 13 (d) 15
  11. 11.What is the 14th term of the AP 12, 20, 28, 36, …? (a) 124 (b) 116 (c) 104 (d) 112
  12. 12.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 370 (b) 740 (c) 64 (d) 400
  13. 13.Which term of the AP 2, 6, 10, 14, … is 70? (a) 18th (b) 17th (c) 20th (d) 19th
  14. 14.Which term of the AP 11, 15, 19, 23, … is 123? (a) 29th (b) 31st (c) 28th (d) 30th
  15. 15.What is the 34th term of the AP 3, 8, 13, 18, …? (a) 173 (b) 165 (c) 168 (d) 170
  16. 16.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 55 (c) 67 (d) 132
  17. 17.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 77 (b) 154 (c) 84 (d) 17
  18. 18.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 6806 (c) 3362 (d) 3321
  19. 19.What is the 18th term of the AP 1, 3, 5, 7, …? (a) 37 (b) 35 (c) 36 (d) 34
  20. 20.Which term of the AP 7, 9, 11, 13, … is 45? (a) 21st (b) 20th (c) 19th (d) 22nd
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
  22. 22.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4186 (c) 4232 (d) 4278
  23. 23.Which term of the AP 18, 22, 26, 30, … is 146? (a) 34th (b) 35th (c) 33rd (d) 32nd
  24. 24.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 1122 (c) 561 (d) 528
  25. 25.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 20 (b) 84 (c) 150 (d) 75
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 72 (d) 64
  27. 27.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 55 (d) 784
  28. 28.What is the 11th term of the AP 7, 9, 11, 13, …? (a) 22 (b) 29 (c) 20 (d) 27
  29. 29.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 384 (b) 708 (c) 57 (d) 354
  30. 30.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 406 (c) 378 (d) 392
  31. 31.What is the 12th term of the AP 12, 16, 20, 24, …? (a) 44 (b) 48 (c) 56 (d) 60
  32. 32.What is the 13th term of the AP 5, 7, 9, 11, …? (a) 26 (b) 31 (c) 24 (d) 29
  33. 33.What is the 21st term of the AP 5, 12, 19, 26, …? (a) 152 (b) 145 (c) 140 (d) 147
  34. 34.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 63 (b) 396 (c) 726 (d) 363
  35. 35.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3240 (c) 3322 (d) 3321
  36. 36.What is the 36th term of the AP 3, 8, 13, 18, …? (a) 183 (b) 180 (c) 178 (d) 175
  37. 37.What is the 15th term of the AP 12, 21, 30, 39, …? (a) 135 (b) 138 (c) 147 (d) 126
  38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  39. 39.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 27 (b) 20 (c) 19 (d) 21
  40. 40.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 80 (b) 83 (c) 160 (d) 22

Answer key

  1. 200
  2. 361
  3. 62
  4. 26th
  5. 14th
  6. 1378
  7. 126
  8. 8th
  9. 26th
  10. 14
  11. 116
  12. 370
  13. 18th
  14. 29th
  15. 168
  16. 66
  17. 77
  18. 3403
  19. 35
  20. 20th
  21. 36
  22. 4278
  23. 33rd
  24. 561
  25. 75
  26. 64
  27. 784
  28. 27
  29. 354
  30. 406
  31. 56
  32. 29
  33. 145
  34. 363
  35. 3321
  36. 178
  37. 138
  38. 121
  39. 20
  40. 80

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