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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 850 · 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 38th term of the AP 5, 8, 11, 14, …? (a) 116 (b) 119 (c) 111 (d) 114
  2. 2.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 13 (b) 8 (c) 7 (d) 6
  3. 3.What is the 36th term of the AP 13, 21, 29, 37, …? (a) 280 (b) 301 (c) 293 (d) 288
  4. 4.Which term of the AP 10, 12, 14, 16, … is 44? (a) 19th (b) 22nd (c) 17th (d) 18th
  5. 5.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 70 (c) 85 (d) 140
  6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 66 (d) 132
  7. 7.Which term of the AP 4, 9, 14, 19, … is 69? (a) 13th (b) 15th (c) 16th (d) 14th
  8. 8.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 26 (b) 34 (c) 27 (d) 25
  9. 9.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 47 (b) 208 (c) 232 (d) 416
  10. 10.What is the 25th term of the AP 13, 18, 23, 28, …? (a) 133 (b) 138 (c) 120 (d) 125
  11. 11.What is the missing term in the AP 14, 21, ?, 35, 42? (a) 29 (b) 27 (c) 35 (d) 28
  12. 12.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2851 (c) 5700 (d) 2850
  13. 13.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 384 (b) 408 (c) 54 (d) 768
  14. 14.What is the 20th term of the AP 8, 17, 26, 35, …? (a) 171 (b) 179 (c) 180 (d) 188
  15. 15.Which term of the AP 4, 6, 8, 10, … is 52? (a) 26th (b) 27th (c) 24th (d) 25th
  16. 16.Which term of the AP 11, 19, 27, 35, … is 211? (a) 27th (b) 25th (c) 26th (d) 28th
  17. 17.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  18. 18.What is the missing term in the AP 20, 29, ?, 47, 56? (a) 37 (b) 47 (c) 39 (d) 38
  19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 39 (d) 210
  20. 20.What is the 26th term of the AP 6, 10, 14, 18, …? (a) 110 (b) 100 (c) 104 (d) 106
  21. 21.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 27 (b) 7 (c) 30 (d) 54
  22. 22.What is the 13th term of the AP 13, 17, 21, 25, …? (a) 61 (b) 65 (c) 52 (d) 48
  23. 23.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 100 (b) 15 (c) 198 (d) 99
  24. 24.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 55 (b) 19 (c) 110 (d) 65
  25. 25.What is the 13th term of the AP 6, 9, 12, 15, …? (a) 39 (b) 36 (c) 45 (d) 42
  26. 26.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
  27. 27.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
  28. 28.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 120 (c) 105 (d) 121
  29. 29.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 666 (c) 703 (d) 704
  30. 30.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 2070 (c) 1035 (d) 990
  31. 31.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 36 (b) 33 (c) 8 (d) 66
  32. 32.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 10 (b) 7 (c) 9 (d) 8
  33. 33.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 2352 (c) 1152 (d) 1176
  34. 34.What is the 37th term of the AP 13, 21, 29, 37, …? (a) 288 (b) 296 (c) 309 (d) 301
  35. 35.Which term of the AP 9, 12, 15, 18, … is 114? (a) 38th (b) 37th (c) 35th (d) 36th
  36. 36.What is the 37th term of the AP 9, 12, 15, 18, …? (a) 111 (b) 120 (c) 117 (d) 108
  37. 37.What is the 33rd term of the AP 8, 14, 20, 26, …? (a) 192 (b) 206 (c) 200 (d) 198
  38. 38.What is the 12th term of the AP 12, 16, 20, 24, …? (a) 48 (b) 56 (c) 44 (d) 60
  39. 39.What is the 13th term of the AP 14, 23, 32, 41, …? (a) 108 (b) 122 (c) 117 (d) 131
  40. 40.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 3698 (c) 7482 (d) 3741

Answer key

  1. 116
  2. 7
  3. 293
  4. 18th
  5. 70
  6. 121
  7. 14th
  8. 26
  9. 208
  10. 133
  11. 28
  12. 2850
  13. 384
  14. 179
  15. 25th
  16. 26th
  17. 256
  18. 38
  19. 400
  20. 106
  21. 27
  22. 61
  23. 99
  24. 55
  25. 42
  26. 225
  27. 361
  28. 120
  29. 703
  30. 1035
  31. 33
  32. 8
  33. 1176
  34. 301
  35. 36th
  36. 117
  37. 200
  38. 56
  39. 122
  40. 3741

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