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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 300 · 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 6 terms of the AP 10, 15, 20, …? (a) 135 (b) 35 (c) 150 (d) 270
  2. 2.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4418 (c) 4465 (d) 4371
  3. 3.Which term of the AP 14, 23, 32, 41, … is 257? (a) 30th (b) 28th (c) 29th (d) 27th
  4. 4.What is the 20th term of the AP 15, 21, 27, 33, …? (a) 135 (b) 120 (c) 114 (d) 129
  5. 5.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 150 (b) 75 (c) 85 (d) 23
  6. 6.What is the 35th term of the AP 15, 18, 21, 24, …? (a) 105 (b) 120 (c) 102 (d) 117
  7. 7.Which term of the AP 5, 11, 17, 23, … is 209? (a) 36th (b) 37th (c) 34th (d) 35th
  8. 8.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 280 (b) 44 (c) 260 (d) 520
  9. 9.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 144 (b) 132 (c) 27 (d) 264
  10. 10.What is the 17th term of the AP 5, 8, 11, 14, …? (a) 56 (b) 51 (c) 48 (d) 53
  11. 11.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 22 (b) 16 (c) 17 (d) 15
  12. 12.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 276 (d) 529
  13. 13.What is the missing term in the AP 5, 14, ?, 32, 41? (a) 22 (b) 23 (c) 32 (d) 24
  14. 14.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 160 (b) 24 (c) 150 (d) 300
  15. 15.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 80 (b) 26 (c) 85 (d) 160
  16. 16.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 6 (b) 8 (c) 7 (d) 9
  17. 17.What is the 34th term of the AP 14, 21, 28, 35, …? (a) 245 (b) 231 (c) 252 (d) 238
  18. 18.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 2352 (c) 1176 (d) 1152
  19. 19.What is the 16th term of the AP 11, 16, 21, 26, …? (a) 91 (b) 86 (c) 75 (d) 80
  20. 20.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 2485 (c) 2556 (d) 5112
  21. 21.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
  22. 22.What is the 19th term of the AP 17, 20, 23, 26, …? (a) 74 (b) 57 (c) 71 (d) 54
  23. 23.What is the 29th term of the AP 2, 8, 14, 20, …? (a) 168 (b) 170 (c) 174 (d) 176
  24. 24.What is the 35th term of the AP 10, 12, 14, 16, …? (a) 68 (b) 70 (c) 80 (d) 78
  25. 25.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  26. 26.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 8 (b) 13 (c) 7 (d) 6
  27. 27.What is the 13th term of the AP 6, 10, 14, 18, …? (a) 48 (b) 52 (c) 54 (d) 58
  28. 28.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 65 (b) 130 (c) 70 (d) 11
  29. 29.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 42 (b) 21 (c) 24 (d) 6
  30. 30.What is the missing term in the AP 16, 19, 22, ?, 28? (a) 25 (b) 26 (c) 24 (d) 28
  31. 31.Which term of the AP 19, 23, 27, 31, … is 139? (a) 30th (b) 31st (c) 33rd (d) 32nd
  32. 32.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
  33. 33.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 108 (b) 198 (c) 24 (d) 99
  34. 34.What is the 39th term of the AP 18, 24, 30, 36, …? (a) 246 (b) 234 (c) 252 (d) 228
  35. 35.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4753 (c) 4656 (d) 9506
  36. 36.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 210 (d) 39
  37. 37.What is the 29th term of the AP 13, 15, 17, 19, …? (a) 71 (b) 56 (c) 58 (d) 69
  38. 38.What is the 40th term of the AP 13, 16, 19, 22, …? (a) 130 (b) 133 (c) 120 (d) 117
  39. 39.What is the 28th term of the AP 12, 21, 30, 39, …? (a) 243 (b) 264 (c) 252 (d) 255
  40. 40.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 8 (b) 6 (c) 7 (d) 10

Answer key

  1. 135
  2. 4465
  3. 28th
  4. 129
  5. 75
  6. 117
  7. 35th
  8. 260
  9. 132
  10. 53
  11. 16
  12. 529
  13. 23
  14. 150
  15. 80
  16. 7
  17. 245
  18. 1176
  19. 86
  20. 2556
  21. 49
  22. 71
  23. 170
  24. 78
  25. 196
  26. 7
  27. 54
  28. 65
  29. 21
  30. 25
  31. 31st
  32. 25
  33. 99
  34. 246
  35. 4753
  36. 400
  37. 69
  38. 130
  39. 255
  40. 7

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