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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 923 · 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 all the whole numbers from 1 to 51? (a) 1275 (b) 2652 (c) 1327 (d) 1326
  2. 2.What is the 37th term of the AP 4, 9, 14, 19, …? (a) 180 (b) 185 (c) 189 (d) 184
  3. 3.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 17 (b) 13 (c) 11 (d) 12
  4. 4.What is the 14th term of the AP 10, 15, 20, 25, …? (a) 75 (b) 65 (c) 80 (d) 70
  5. 5.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  6. 6.What is the 33rd term of the AP 9, 11, 13, 15, …? (a) 75 (b) 73 (c) 66 (d) 64
  7. 7.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3916 (c) 3872 (d) 7832
  8. 8.What is the 39th term of the AP 14, 22, 30, 38, …? (a) 304 (b) 312 (c) 326 (d) 318
  9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 169 (c) 25 (d) 182
  10. 10.Which term of the AP 6, 11, 16, 21, … is 161? (a) 34th (b) 33rd (c) 32nd (d) 31st
  11. 11.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 1081 (c) 1129 (d) 2256
  12. 12.What is the sum of all the whole numbers from 1 to 90? (a) 8190 (b) 4005 (c) 4050 (d) 4095
  13. 13.Which term of the AP 19, 22, 25, 28, … is 46? (a) 11th (b) 12th (c) 10th (d) 9th
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  15. 15.What is the 19th term of the AP 8, 10, 12, 14, …? (a) 36 (b) 38 (c) 46 (d) 44
  16. 16.What is the 23rd term of the AP 18, 21, 24, 27, …? (a) 84 (b) 87 (c) 69 (d) 66
  17. 17.Which term of the AP 9, 13, 17, 21, … is 161? (a) 38th (b) 41st (c) 39th (d) 40th
  18. 18.What is the 15th term of the AP 10, 13, 16, 19, …? (a) 42 (b) 52 (c) 55 (d) 45
  19. 19.What is the 21st term of the AP 2, 11, 20, 29, …? (a) 191 (b) 189 (c) 180 (d) 182
  20. 20.Which term of the AP 1, 6, 11, 16, … is 181? (a) 38th (b) 39th (c) 36th (d) 37th
  21. 21.Which term of the AP 4, 6, 8, 10, … is 22? (a) 12th (b) 9th (c) 11th (d) 10th
  22. 22.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1431 (c) 2862 (d) 1432
  23. 23.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 208 (b) 47 (c) 232 (d) 416
  24. 24.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 210 (b) 33 (c) 390 (d) 195
  25. 25.Which term of the AP 15, 19, 23, 27, … is 155? (a) 38th (b) 36th (c) 37th (d) 35th
  26. 26.What is the missing term in the AP 19, 25, 31, ?, 43? (a) 38 (b) 37 (c) 36 (d) 43
  27. 27.Which term of the AP 10, 12, 14, 16, … is 60? (a) 30th (b) 25th (c) 26th (d) 27th
  28. 28.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 27 (b) 35 (c) 26 (d) 28
  29. 29.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 190 (b) 200 (c) 380 (d) 28
  30. 30.What is the 34th term of the AP 4, 8, 12, 16, …? (a) 137 (b) 132 (c) 140 (d) 136
  31. 31.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 240 (b) 31 (c) 252 (d) 480
  32. 32.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 27 (b) 25 (c) 26 (d) 34
  33. 33.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 55 (b) 10 (c) 60 (d) 110
  34. 34.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 198 (b) 209 (c) 28 (d) 396
  35. 35.What is the 12th term of the AP 6, 12, 18, 24, …? (a) 73 (b) 78 (c) 66 (d) 72
  36. 36.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 99 (b) 198 (c) 100 (d) 15
  37. 37.Which term of the AP 12, 17, 22, 27, … is 182? (a) 36th (b) 37th (c) 35th (d) 34th
  38. 38.What is the 10th term of the AP 15, 17, 19, 21, …? (a) 35 (b) 20 (c) 33 (d) 18
  39. 39.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 1122 (c) 561 (d) 562
  40. 40.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 22 (b) 30 (c) 21 (d) 23

Answer key

  1. 1326
  2. 184
  3. 12
  4. 75
  5. 576
  6. 73
  7. 3916
  8. 318
  9. 169
  10. 32nd
  11. 1128
  12. 4095
  13. 10th
  14. 121
  15. 44
  16. 84
  17. 39th
  18. 52
  19. 182
  20. 37th
  21. 10th
  22. 1431
  23. 208
  24. 195
  25. 36th
  26. 37
  27. 26th
  28. 27
  29. 190
  30. 136
  31. 240
  32. 26
  33. 55
  34. 198
  35. 72
  36. 99
  37. 35th
  38. 33
  39. 561
  40. 22

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