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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 630 · 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 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  2. 2.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 65 (b) 60 (c) 120 (d) 16
  3. 3.What is the 38th term of the AP 1, 9, 17, 25, …? (a) 296 (b) 305 (c) 304 (d) 297
  4. 4.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 184 (b) 328 (c) 38 (d) 164
  5. 5.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 33 (b) 26 (c) 24 (d) 25
  6. 6.What is the 35th term of the AP 20, 25, 30, 35, …? (a) 190 (b) 195 (c) 170 (d) 175
  7. 7.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 864 (b) 69 (c) 432 (d) 468
  8. 8.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 196 (b) 112 (c) 26 (d) 98
  9. 9.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 28 (b) 22 (c) 20 (d) 21
  10. 10.What is the 33rd term of the AP 6, 11, 16, 21, …? (a) 171 (b) 165 (c) 160 (d) 166
  11. 11.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 30 (b) 38 (c) 29 (d) 28
  12. 12.What is the 24th term of the AP 9, 18, 27, 36, …? (a) 207 (b) 217 (c) 216 (d) 225
  13. 13.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 47 (b) 319 (c) 594 (d) 297
  14. 14.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 220 (b) 440 (c) 223 (d) 35
  15. 15.What is the 13th term of the AP 8, 10, 12, 14, …? (a) 34 (b) 32 (c) 26 (d) 24
  16. 16.What is the 29th term of the AP 4, 8, 12, 16, …? (a) 112 (b) 117 (c) 116 (d) 120
  17. 17.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 33 (b) 34 (c) 32 (d) 41
  18. 18.What is the missing term in the AP 4, 12, 20, ?, 36? (a) 29 (b) 27 (c) 36 (d) 28
  19. 19.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 960 (b) 73 (c) 480 (d) 516
  20. 20.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  21. 21.Which term of the AP 15, 23, 31, 39, … is 95? (a) 10th (b) 13th (c) 11th (d) 12th
  22. 22.Which term of the AP 12, 17, 22, 27, … is 207? (a) 40th (b) 42nd (c) 41st (d) 39th
  23. 23.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 260 (c) 470 (d) 235
  24. 24.What is the 25th term of the AP 16, 19, 22, 25, …? (a) 91 (b) 88 (c) 72 (d) 75
  25. 25.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 18 (b) 19 (c) 23 (d) 20
  26. 26.What is the 10th term of the AP 13, 22, 31, 40, …? (a) 103 (b) 81 (c) 90 (d) 94
  27. 27.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 6320 (c) 3160 (d) 3081
  28. 28.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  29. 29.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 19 (b) 17 (c) 25 (d) 18
  30. 30.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 468 (b) 50 (c) 261 (d) 234
  31. 31.Which term of the AP 20, 22, 24, 26, … is 80? (a) 40th (b) 31st (c) 32nd (d) 30th
  32. 32.What is the 13th term of the AP 11, 13, 15, 17, …? (a) 37 (b) 26 (c) 35 (d) 24
  33. 33.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 10 (b) 11 (c) 12 (d) 18
  34. 34.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 48 (b) 39 (c) 41 (d) 40
  35. 35.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 108 (c) 216 (d) 109
  36. 36.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 120 (b) 240 (c) 128 (d) 22
  37. 37.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 148 (b) 36 (c) 296 (d) 168
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 25 (c) 9 (d) 15
  39. 39.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 120 (b) 60 (c) 22 (d) 65
  40. 40.What is the 22nd term of the AP 20, 26, 32, 38, …? (a) 146 (b) 152 (c) 132 (d) 126

Answer key

  1. 121
  2. 60
  3. 297
  4. 164
  5. 25
  6. 190
  7. 432
  8. 98
  9. 21
  10. 166
  11. 29
  12. 216
  13. 297
  14. 220
  15. 32
  16. 116
  17. 33
  18. 28
  19. 480
  20. 49
  21. 11th
  22. 40th
  23. 235
  24. 88
  25. 19
  26. 94
  27. 3160
  28. 144
  29. 18
  30. 234
  31. 31st
  32. 35
  33. 11
  34. 40
  35. 108
  36. 120
  37. 148
  38. 25
  39. 60
  40. 146

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