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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 806 · 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 12 terms of the AP 2, 6, 10, …? (a) 312 (b) 46 (c) 288 (d) 576
  2. 2.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 21 (b) 22 (c) 28 (d) 23
  3. 3.What is the 17th term of the AP 12, 19, 26, 33, …? (a) 112 (b) 124 (c) 131 (d) 119
  4. 4.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 305 (b) 53 (c) 610 (d) 330
  5. 5.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 4 (b) 3 (c) 6 (d) 5
  6. 6.What is the 13th term of the AP 1, 6, 11, 16, …? (a) 65 (b) 60 (c) 66 (d) 61
  7. 7.What is the 27th term of the AP 9, 17, 25, 33, …? (a) 216 (b) 225 (c) 208 (d) 217
  8. 8.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 160 (b) 26 (c) 85 (d) 80
  9. 9.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 380 (b) 350 (c) 700 (d) 62
  10. 10.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3321 (c) 6806 (d) 3403
  11. 11.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 252 (b) 33 (c) 131 (d) 126
  12. 12.What is the 34th term of the AP 1, 9, 17, 25, …? (a) 273 (b) 265 (c) 272 (d) 264
  13. 13.What is the 14th term of the AP 20, 22, 24, 26, …? (a) 46 (b) 26 (c) 48 (d) 28
  14. 14.What is the 18th term of the AP 3, 7, 11, 15, …? (a) 72 (b) 68 (c) 71 (d) 75
  15. 15.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 240 (c) 120 (d) 121
  16. 16.What is the 17th term of the AP 18, 21, 24, 27, …? (a) 51 (b) 66 (c) 69 (d) 48
  17. 17.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 192 (b) 180 (c) 26 (d) 360
  18. 18.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 325 (d) 300
  19. 19.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4372 (c) 4371 (d) 4278
  20. 20.Which term of the AP 1, 3, 5, 7, … is 31? (a) 18th (b) 15th (c) 16th (d) 17th
  21. 21.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 14 (c) 108 (d) 102
  22. 22.What is the 40th term of the AP 1, 9, 17, 25, …? (a) 321 (b) 312 (c) 320 (d) 313
  23. 23.Which term of the AP 2, 6, 10, 14, … is 138? (a) 36th (b) 34th (c) 37th (d) 35th
  24. 24.What is the 11th term of the AP 5, 7, 9, 11, …? (a) 22 (b) 25 (c) 27 (d) 20
  25. 25.Which term of the AP 18, 22, 26, 30, … is 98? (a) 20th (b) 22nd (c) 23rd (d) 21st
  26. 26.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 36 (b) 31 (c) 30 (d) 29
  27. 27.What is the 13th term of the AP 1, 3, 5, 7, …? (a) 27 (b) 24 (c) 25 (d) 26
  28. 28.What is the 36th term of the AP 20, 24, 28, 32, …? (a) 160 (b) 164 (c) 144 (d) 140
  29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  30. 30.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 200 (b) 32 (c) 115 (d) 100
  31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 812 (d) 406
  32. 32.What is the 27th term of the AP 8, 17, 26, 35, …? (a) 242 (b) 251 (c) 243 (d) 234
  33. 33.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 65 (b) 130 (c) 80 (d) 25
  34. 34.Which term of the AP 10, 15, 20, 25, … is 45? (a) 7th (b) 10th (c) 9th (d) 8th
  35. 35.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 72 (d) 36
  36. 36.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 360 (b) 390 (c) 63 (d) 720
  37. 37.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1485 (c) 1431 (d) 2970
  38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
  39. 39.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 92 (b) 184 (c) 96 (d) 15
  40. 40.What is the 10th term of the AP 8, 11, 14, 17, …? (a) 30 (b) 38 (c) 27 (d) 35

Answer key

  1. 288
  2. 22
  3. 124
  4. 305
  5. 4
  6. 61
  7. 217
  8. 80
  9. 350
  10. 3403
  11. 126
  12. 265
  13. 46
  14. 71
  15. 120
  16. 66
  17. 180
  18. 325
  19. 4371
  20. 16th
  21. 102
  22. 313
  23. 35th
  24. 25
  25. 21st
  26. 30
  27. 25
  28. 160
  29. 100
  30. 100
  31. 784
  32. 242
  33. 65
  34. 8th
  35. 64
  36. 360
  37. 1485
  38. 121
  39. 92
  40. 35

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