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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 965 · 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 14th term of the AP 14, 22, 30, 38, …? (a) 112 (b) 126 (c) 118 (d) 104
  2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 42 (d) 11
  3. 3.Which term of the AP 20, 23, 26, 29, … is 134? (a) 40th (b) 38th (c) 39th (d) 41st
  4. 4.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 55 (c) 67 (d) 132
  5. 5.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1596 (c) 1568 (d) 1540
  6. 6.Which term of the AP 8, 16, 24, 32, … is 88? (a) 10th (b) 13th (c) 11th (d) 12th
  7. 7.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 49 (d) 625
  8. 8.What is the 36th term of the AP 12, 18, 24, 30, …? (a) 210 (b) 228 (c) 216 (d) 222
  9. 9.Which term of the AP 9, 17, 25, 33, … is 201? (a) 27th (b) 25th (c) 26th (d) 24th
  10. 10.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 171 (d) 324
  11. 11.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 31 (b) 38 (c) 29 (d) 30
  12. 12.Which term of the AP 4, 13, 22, 31, … is 193? (a) 21st (b) 24th (c) 22nd (d) 23rd
  13. 13.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 384 (b) 192 (c) 208 (d) 38
  14. 14.Which term of the AP 13, 20, 27, 34, … is 125? (a) 16th (b) 19th (c) 17th (d) 18th
  15. 15.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 59 (b) 748 (c) 379 (d) 374
  16. 16.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 173 (b) 336 (c) 168 (d) 39
  17. 17.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 176 (b) 320 (c) 160 (d) 34
  18. 18.What is the 19th term of the AP 14, 22, 30, 38, …? (a) 152 (b) 166 (c) 158 (d) 144
  19. 19.Which term of the AP 10, 13, 16, 19, … is 73? (a) 24th (b) 22nd (c) 21st (d) 23rd
  20. 20.Which term of the AP 3, 11, 19, 27, … is 83? (a) 11th (b) 10th (c) 12th (d) 13th
  21. 21.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 136 (d) 31
  22. 22.Which term of the AP 7, 15, 23, 31, … is 247? (a) 33rd (b) 32nd (c) 31st (d) 30th
  23. 23.What is the 25th term of the AP 4, 9, 14, 19, …? (a) 124 (b) 120 (c) 125 (d) 129
  24. 24.Which term of the AP 10, 15, 20, 25, … is 65? (a) 12th (b) 14th (c) 13th (d) 11th
  25. 25.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 264 (b) 132 (c) 27 (d) 144
  26. 26.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 21 (b) 15 (c) 16 (d) 17
  27. 27.What is the 18th term of the AP 6, 8, 10, 12, …? (a) 34 (b) 40 (c) 36 (d) 42
  28. 28.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 25 (b) 27 (c) 26 (d) 29
  29. 29.What is the 13th term of the AP 15, 20, 25, 30, …? (a) 80 (b) 60 (c) 65 (d) 75
  30. 30.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 310 (b) 570 (c) 285 (d) 51
  31. 31.What is the 10th term of the AP 17, 23, 29, 35, …? (a) 54 (b) 77 (c) 71 (d) 60
  32. 32.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 60 (b) 54 (c) 14 (d) 108
  33. 33.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 238 (b) 124 (c) 119 (d) 32
  34. 34.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 26 (b) 24 (c) 22 (d) 23
  35. 35.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 51 (b) 54 (c) 102 (d) 11
  36. 36.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 168 (b) 15 (c) 85 (d) 84
  37. 37.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1653 (c) 1654 (d) 1596
  38. 38.What is the 10th term of the AP 3, 12, 21, 30, …? (a) 93 (b) 84 (c) 81 (d) 90
  39. 39.What is the 34th term of the AP 16, 21, 26, 31, …? (a) 181 (b) 165 (c) 170 (d) 186
  40. 40.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 9 (b) 8 (c) 10 (d) 14

Answer key

  1. 118
  2. 36
  3. 39th
  4. 66
  5. 1596
  6. 11th
  7. 625
  8. 222
  9. 25th
  10. 324
  11. 30
  12. 22nd
  13. 192
  14. 17th
  15. 374
  16. 168
  17. 160
  18. 158
  19. 22nd
  20. 11th
  21. 256
  22. 31st
  23. 124
  24. 12th
  25. 132
  26. 16
  27. 40
  28. 26
  29. 75
  30. 285
  31. 71
  32. 54
  33. 119
  34. 23
  35. 51
  36. 84
  37. 1653
  38. 84
  39. 181
  40. 9

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