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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 290 · 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 2, 6, 10, …? (a) 256 (b) 30 (c) 144 (d) 128
  2. 2.What is the 37th term of the AP 18, 27, 36, 45, …? (a) 333 (b) 324 (c) 342 (d) 351
  3. 3.What is the 17th term of the AP 3, 12, 21, 30, …? (a) 144 (b) 156 (c) 153 (d) 147
  4. 4.What is the 27th term of the AP 6, 8, 10, 12, …? (a) 58 (b) 60 (c) 54 (d) 52
  5. 5.What is the 21st term of the AP 7, 13, 19, 25, …? (a) 126 (b) 127 (c) 120 (d) 133
  6. 6.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 192 (b) 352 (c) 36 (d) 176
  7. 7.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 29 (d) 120
  8. 8.What is the 18th term of the AP 7, 9, 11, 13, …? (a) 34 (b) 43 (c) 36 (d) 41
  9. 9.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 160 (b) 24 (c) 150 (d) 300
  10. 10.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 112 (b) 31 (c) 224 (d) 117
  11. 11.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 28 (b) 21 (c) 22 (d) 20
  12. 12.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 22 (b) 20 (c) 24 (d) 21
  13. 13.What is the 35th term of the AP 11, 16, 21, 26, …? (a) 186 (b) 181 (c) 175 (d) 170
  14. 14.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 26 (b) 25 (c) 24 (d) 33
  15. 15.What is the 24th term of the AP 16, 23, 30, 37, …? (a) 184 (b) 177 (c) 168 (d) 161
  16. 16.Which term of the AP 6, 10, 14, 18, … is 150? (a) 38th (b) 36th (c) 39th (d) 37th
  17. 17.Which term of the AP 10, 15, 20, 25, … is 170? (a) 34th (b) 35th (c) 33rd (d) 32nd
  18. 18.What is the 19th term of the AP 5, 7, 9, 11, …? (a) 38 (b) 43 (c) 41 (d) 36
  19. 19.What is the 22nd term of the AP 13, 20, 27, 34, …? (a) 154 (b) 167 (c) 147 (d) 160
  20. 20.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4371 (c) 4418 (d) 8930
  21. 21.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 3200 (c) 6480 (d) 3160
  22. 22.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 880 (b) 70 (c) 440 (d) 473
  23. 23.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4561 (c) 4465 (d) 4560
  24. 24.What is the 11th term of the AP 2, 8, 14, 20, …? (a) 66 (b) 62 (c) 60 (d) 68
  25. 25.What is the 40th term of the AP 1, 6, 11, 16, …? (a) 195 (b) 201 (c) 196 (d) 200
  26. 26.What is the 37th term of the AP 9, 14, 19, 24, …? (a) 194 (b) 185 (c) 189 (d) 180
  27. 27.What is the 10th term of the AP 12, 16, 20, 24, …? (a) 36 (b) 48 (c) 52 (d) 40
  28. 28.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 26 (b) 28 (c) 32 (d) 27
  29. 29.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 66 (b) 36 (c) 33 (d) 8
  30. 30.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 406 (c) 55 (d) 812
  31. 31.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 210 (b) 189 (c) 45 (d) 378
  32. 32.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 650 (d) 325
  33. 33.Which term of the AP 5, 11, 17, 23, … is 119? (a) 19th (b) 22nd (c) 21st (d) 20th
  34. 34.What is the 21st term of the AP 15, 18, 21, 24, …? (a) 75 (b) 78 (c) 63 (d) 60
  35. 35.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 2628 (c) 5256 (d) 2556
  36. 36.What is the missing term in the AP 9, 11, ?, 15, 17? (a) 12 (b) 14 (c) 13 (d) 15
  37. 37.What is the 11th term of the AP 13, 20, 27, 34, …? (a) 70 (b) 90 (c) 77 (d) 83
  38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  39. 39.What is the 25th term of the AP 2, 5, 8, 11, …? (a) 74 (b) 72 (c) 77 (d) 75
  40. 40.What is the 14th term of the AP 3, 11, 19, 27, …? (a) 112 (b) 115 (c) 104 (d) 107

Answer key

  1. 128
  2. 342
  3. 147
  4. 58
  5. 127
  6. 176
  7. 225
  8. 41
  9. 150
  10. 112
  11. 21
  12. 21
  13. 181
  14. 25
  15. 177
  16. 37th
  17. 33rd
  18. 41
  19. 160
  20. 4465
  21. 3240
  22. 440
  23. 4560
  24. 62
  25. 196
  26. 189
  27. 48
  28. 27
  29. 33
  30. 784
  31. 189
  32. 625
  33. 20th
  34. 75
  35. 2628
  36. 13
  37. 83
  38. 121
  39. 74
  40. 107

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