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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 5 · 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 44? (a) 990 (b) 968 (c) 946 (d) 1980
  2. 2.What is the 39th term of the AP 15, 17, 19, 21, …? (a) 93 (b) 76 (c) 91 (d) 78
  3. 3.What is the 18th term of the AP 1, 10, 19, 28, …? (a) 153 (b) 162 (c) 154 (d) 163
  4. 4.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 22 (b) 135 (c) 252 (d) 126
  5. 5.What is the 15th term of the AP 8, 10, 12, 14, …? (a) 28 (b) 36 (c) 38 (d) 30
  6. 6.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 21 (b) 20 (c) 22 (d) 24
  7. 7.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 266 (b) 49 (c) 522 (d) 261
  8. 8.What is the missing term in the AP 15, ?, 19, 21, 23? (a) 16 (b) 18 (c) 17 (d) 19
  9. 9.What is the 26th term of the AP 20, 26, 32, 38, …? (a) 150 (b) 176 (c) 170 (d) 156
  10. 10.What is the 37th term of the AP 16, 23, 30, 37, …? (a) 275 (b) 252 (c) 268 (d) 259
  11. 11.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 300 (b) 600 (c) 330 (d) 57
  12. 12.What is the 11th term of the AP 15, 18, 21, 24, …? (a) 30 (b) 33 (c) 45 (d) 48
  13. 13.What is the 26th term of the AP 1, 8, 15, 22, …? (a) 175 (b) 176 (c) 182 (d) 183
  14. 14.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 154 (b) 168 (c) 34 (d) 308
  15. 15.What is the 16th term of the AP 7, 10, 13, 16, …? (a) 45 (b) 48 (c) 52 (d) 55
  16. 16.Which term of the AP 5, 11, 17, 23, … is 47? (a) 8th (b) 7th (c) 10th (d) 9th
  17. 17.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 11 (b) 10 (c) 12 (d) 13
  18. 18.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 1541 (c) 1485 (d) 3080
  19. 19.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 19 (b) 17 (c) 22 (d) 18
  20. 20.What is the 17th term of the AP 12, 16, 20, 24, …? (a) 76 (b) 64 (c) 80 (d) 68
  21. 21.What is the 33rd term of the AP 7, 15, 23, 31, …? (a) 264 (b) 263 (c) 271 (d) 256
  22. 22.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
  23. 23.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 312 (b) 30 (c) 156 (d) 168
  24. 24.What is the 33rd term of the AP 3, 6, 9, 12, …? (a) 96 (b) 102 (c) 100 (d) 99
  25. 25.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 432 (b) 864 (c) 468 (d) 69
  26. 26.What is the 18th term of the AP 12, 18, 24, 30, …? (a) 108 (b) 120 (c) 102 (d) 114
  27. 27.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 512 (c) 1056 (d) 496
  28. 28.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 12 (b) 60 (c) 57 (d) 114
  29. 29.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 5402 (c) 2702 (d) 2701
  30. 30.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 104 (b) 184 (c) 22 (d) 92
  31. 31.Which term of the AP 6, 10, 14, 18, … is 86? (a) 20th (b) 23rd (c) 22nd (d) 21st
  32. 32.What is the 35th term of the AP 12, 14, 16, 18, …? (a) 82 (b) 70 (c) 68 (d) 80
  33. 33.What is the 12th term of the AP 1, 7, 13, 19, …? (a) 66 (b) 67 (c) 73 (d) 72
  34. 34.What is the 10th term of the AP 11, 13, 15, 17, …? (a) 31 (b) 20 (c) 18 (d) 29
  35. 35.What is the 27th term of the AP 12, 16, 20, 24, …? (a) 108 (b) 116 (c) 104 (d) 120
  36. 36.What is the 37th term of the AP 14, 16, 18, 20, …? (a) 72 (b) 74 (c) 88 (d) 86
  37. 37.Which term of the AP 15, 17, 19, 21, … is 53? (a) 19th (b) 22nd (c) 20th (d) 21st
  38. 38.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4278 (c) 4232 (d) 4186
  39. 39.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 21 (d) 36
  40. 40.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 156 (b) 312 (c) 168 (d) 24

Answer key

  1. 990
  2. 91
  3. 154
  4. 126
  5. 36
  6. 21
  7. 261
  8. 17
  9. 170
  10. 268
  11. 300
  12. 45
  13. 176
  14. 154
  15. 52
  16. 8th
  17. 11
  18. 1540
  19. 18
  20. 76
  21. 263
  22. 64
  23. 156
  24. 99
  25. 432
  26. 114
  27. 528
  28. 57
  29. 2701
  30. 92
  31. 21st
  32. 80
  33. 67
  34. 29
  35. 116
  36. 86
  37. 20th
  38. 4278
  39. 36
  40. 156

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