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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 619 · 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 6, 10, 14, …? (a) 176 (b) 34 (c) 160 (d) 320
  2. 2.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 63 (b) 126 (c) 70 (d) 15
  3. 3.Which term of the AP 2, 6, 10, 14, … is 94? (a) 25th (b) 24th (c) 23rd (d) 26th
  4. 4.What is the 25th term of the AP 10, 13, 16, 19, …? (a) 72 (b) 82 (c) 75 (d) 85
  5. 5.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2080 (c) 4160 (d) 2016
  6. 6.What is the 40th term of the AP 17, 22, 27, 32, …? (a) 212 (b) 195 (c) 217 (d) 200
  7. 7.What is the 21st term of the AP 19, 24, 29, 34, …? (a) 105 (b) 124 (c) 119 (d) 100
  8. 8.What is the missing term in the AP 9, 11, 13, ?, 17? (a) 14 (b) 15 (c) 17 (d) 16
  9. 9.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 703 (c) 1406 (d) 704
  10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  11. 11.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 882 (c) 1806 (d) 861
  12. 12.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 252 (b) 234 (c) 468 (d) 42
  13. 13.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 45 (b) 378 (c) 189 (d) 210
  14. 14.Which term of the AP 10, 14, 18, 22, … is 58? (a) 13th (b) 12th (c) 14th (d) 15th
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 210 (d) 400
  16. 16.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 198 (b) 14 (c) 99 (d) 100
  17. 17.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 176 (b) 352 (c) 36 (d) 192
  18. 18.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 19 (b) 145 (c) 150 (d) 290
  19. 19.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 18 (b) 12 (c) 11 (d) 10
  20. 20.What is the 10th term of the AP 19, 27, 35, 43, …? (a) 72 (b) 99 (c) 91 (d) 80
  21. 21.Which term of the AP 6, 9, 12, 15, … is 114? (a) 36th (b) 39th (c) 37th (d) 38th
  22. 22.What is the 38th term of the AP 3, 11, 19, 27, …? (a) 296 (b) 304 (c) 307 (d) 299
  23. 23.What is the missing term in the AP 15, ?, 29, 36, 43? (a) 21 (b) 23 (c) 22 (d) 29
  24. 24.What is the 13th term of the AP 19, 26, 33, 40, …? (a) 103 (b) 91 (c) 84 (d) 110
  25. 25.What is the 13th term of the AP 8, 10, 12, 14, …? (a) 34 (b) 26 (c) 24 (d) 32
  26. 26.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4560 (c) 4465 (d) 4561
  27. 27.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 12 (b) 154 (c) 77 (d) 78
  28. 28.What is the 19th term of the AP 7, 12, 17, 22, …? (a) 97 (b) 90 (c) 95 (d) 102
  29. 29.What is the 27th term of the AP 16, 19, 22, 25, …? (a) 78 (b) 97 (c) 94 (d) 81
  30. 30.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 6006 (c) 2926 (d) 3003
  31. 31.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 192 (b) 372 (c) 21 (d) 186
  32. 32.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 90 (c) 180 (d) 13
  33. 33.What is the 15th term of the AP 20, 27, 34, 41, …? (a) 98 (b) 125 (c) 118 (d) 105
  34. 34.What is the 25th term of the AP 19, 22, 25, 28, …? (a) 94 (b) 75 (c) 91 (d) 72
  35. 35.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 11 (d) 42
  36. 36.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 190 (b) 175 (c) 350 (d) 31
  37. 37.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 132 (b) 120 (c) 30 (d) 240
  38. 38.What is the 34th term of the AP 11, 17, 23, 29, …? (a) 215 (b) 209 (c) 198 (d) 204
  39. 39.What is the 32nd term of the AP 1, 4, 7, 10, …? (a) 93 (b) 96 (c) 94 (d) 97
  40. 40.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 25 (b) 27 (c) 35 (d) 26

Answer key

  1. 160
  2. 63
  3. 24th
  4. 82
  5. 2080
  6. 212
  7. 119
  8. 15
  9. 703
  10. 529
  11. 903
  12. 234
  13. 189
  14. 13th
  15. 400
  16. 99
  17. 176
  18. 145
  19. 11
  20. 91
  21. 37th
  22. 299
  23. 22
  24. 103
  25. 32
  26. 4560
  27. 77
  28. 97
  29. 94
  30. 3003
  31. 186
  32. 90
  33. 118
  34. 91
  35. 36
  36. 175
  37. 120
  38. 209
  39. 94
  40. 26

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