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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 588 · 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 31st term of the AP 4, 8, 12, 16, …? (a) 124 (b) 125 (c) 128 (d) 120
  2. 2.What is the 14th term of the AP 2, 11, 20, 29, …? (a) 126 (b) 128 (c) 119 (d) 117
  3. 3.What is the 11th term of the AP 16, 20, 24, 28, …? (a) 44 (b) 40 (c) 56 (d) 60
  4. 4.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1431 (c) 2970 (d) 1485
  5. 5.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  6. 6.Which term of the AP 2, 8, 14, 20, … is 122? (a) 23rd (b) 22nd (c) 20th (d) 21st
  7. 7.Which term of the AP 10, 15, 20, 25, … is 65? (a) 14th (b) 13th (c) 11th (d) 12th
  8. 8.What is the 29th term of the AP 17, 25, 33, 41, …? (a) 232 (b) 224 (c) 241 (d) 249
  9. 9.Which term of the AP 15, 17, 19, 21, … is 69? (a) 27th (b) 28th (c) 30th (d) 29th
  10. 10.What is the 28th term of the AP 16, 19, 22, 25, …? (a) 97 (b) 84 (c) 81 (d) 100
  11. 11.Which term of the AP 8, 11, 14, 17, … is 89? (a) 27th (b) 29th (c) 30th (d) 28th
  12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 42 (d) 11
  13. 13.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
  14. 14.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 96 (b) 104 (c) 19 (d) 192
  15. 15.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 22 (b) 28 (c) 23 (d) 21
  16. 16.Which term of the AP 13, 15, 17, 19, … is 43? (a) 17th (b) 16th (c) 18th (d) 15th
  17. 17.What is the 38th term of the AP 19, 22, 25, 28, …? (a) 111 (b) 114 (c) 133 (d) 130
  18. 18.What is the 19th term of the AP 10, 17, 24, 31, …? (a) 143 (b) 126 (c) 136 (d) 133
  19. 19.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 120 (b) 128 (c) 22 (d) 240
  20. 20.What is the 13th term of the AP 13, 22, 31, 40, …? (a) 108 (b) 121 (c) 130 (d) 117
  21. 21.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 462 (b) 69 (c) 858 (d) 429
  22. 22.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  23. 23.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 84 (b) 96 (c) 168 (d) 24
  24. 24.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 48 (b) 45 (c) 90 (d) 15
  25. 25.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2278 (c) 4556 (d) 2279
  26. 26.What is the missing term in the AP 4, 9, 14, ?, 24? (a) 19 (b) 20 (c) 18 (d) 24
  27. 27.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1035 (c) 2070 (d) 1036
  28. 28.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 6 (b) 7 (c) 8 (d) 11
  29. 29.Which term of the AP 19, 21, 23, 25, … is 75? (a) 31st (b) 29th (c) 30th (d) 28th
  30. 30.Which term of the AP 18, 22, 26, 30, … is 126? (a) 29th (b) 28th (c) 27th (d) 30th
  31. 31.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 5050 (c) 4950 (d) 10100
  32. 32.Which term of the AP 13, 17, 21, 25, … is 85? (a) 18th (b) 20th (c) 19th (d) 21st
  33. 33.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 27 (b) 26 (c) 28 (d) 34
  34. 34.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  35. 35.Which term of the AP 17, 21, 25, 29, … is 129? (a) 31st (b) 28th (c) 30th (d) 29th
  36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 325 (d) 650
  37. 37.Which term of the AP 2, 5, 8, 11, … is 71? (a) 24th (b) 23rd (c) 25th (d) 26th
  38. 38.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 90 (b) 45 (c) 55 (d) 17
  39. 39.What is the 17th term of the AP 4, 7, 10, 13, …? (a) 52 (b) 48 (c) 55 (d) 51
  40. 40.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1378 (c) 1326 (d) 2756

Answer key

  1. 124
  2. 119
  3. 56
  4. 1485
  5. 121
  6. 21st
  7. 12th
  8. 241
  9. 28th
  10. 97
  11. 28th
  12. 36
  13. 64
  14. 96
  15. 22
  16. 16th
  17. 130
  18. 136
  19. 120
  20. 121
  21. 429
  22. 25
  23. 84
  24. 45
  25. 2278
  26. 19
  27. 1035
  28. 7
  29. 29th
  30. 28th
  31. 5050
  32. 19th
  33. 27
  34. 400
  35. 29th
  36. 625
  37. 24th
  38. 45
  39. 52
  40. 1378

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