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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 368 · 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 34th term of the AP 15, 22, 29, 36, …? (a) 253 (b) 231 (c) 246 (d) 238
  2. 2.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 91 (d) 182
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 42 (d) 21
  4. 4.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 49 (d) 13
  5. 5.What is the 22nd term of the AP 2, 7, 12, 17, …? (a) 105 (b) 110 (c) 107 (d) 112
  6. 6.Which term of the AP 8, 14, 20, 26, … is 50? (a) 9th (b) 8th (c) 10th (d) 7th
  7. 7.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576
  8. 8.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 26 (b) 34 (c) 25 (d) 24
  9. 9.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 1596 (c) 3306 (d) 1653
  10. 10.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 72 (d) 64
  11. 11.What is the 20th term of the AP 2, 10, 18, 26, …? (a) 152 (b) 160 (c) 162 (d) 154
  12. 12.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 325 (c) 300 (d) 650
  13. 13.Which term of the AP 1, 7, 13, 19, … is 139? (a) 26th (b) 24th (c) 23rd (d) 25th
  14. 14.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 108 (b) 60 (c) 54 (d) 14
  15. 15.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 19 (b) 22 (c) 20 (d) 21
  16. 16.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 420 (d) 39
  17. 17.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 1260 (c) 630 (d) 595
  18. 18.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1431 (c) 1378 (d) 1432
  19. 19.Which term of the AP 4, 6, 8, 10, … is 26? (a) 12th (b) 11th (c) 13th (d) 14th
  20. 20.What is the 19th term of the AP 13, 20, 27, 34, …? (a) 146 (b) 126 (c) 133 (d) 139
  21. 21.What is the 19th term of the AP 19, 23, 27, 31, …? (a) 76 (b) 91 (c) 72 (d) 95
  22. 22.What is the 28th term of the AP 14, 16, 18, 20, …? (a) 54 (b) 68 (c) 70 (d) 56
  23. 23.What is the 21st term of the AP 1, 5, 9, 13, …? (a) 80 (b) 81 (c) 85 (d) 84
  24. 24.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 12 (b) 13 (c) 11 (d) 10
  25. 25.What is the sum of all the whole numbers from 1 to 60? (a) 1830 (b) 1770 (c) 1800 (d) 3660
  26. 26.What is the missing term in the AP 11, 18, 25, ?, 39? (a) 32 (b) 33 (c) 39 (d) 31
  27. 27.What is the 10th term of the AP 20, 28, 36, 44, …? (a) 92 (b) 72 (c) 80 (d) 100
  28. 28.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 624 (b) 312 (c) 48 (d) 336
  29. 29.What is the 28th term of the AP 20, 28, 36, 44, …? (a) 224 (b) 236 (c) 244 (d) 216
  30. 30.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 19 (b) 17 (c) 18 (d) 26
  31. 31.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 20 (b) 25 (c) 18 (d) 19
  32. 32.What is the 28th term of the AP 1, 7, 13, 19, …? (a) 169 (b) 163 (c) 162 (d) 168
  33. 33.What is the 27th term of the AP 13, 18, 23, 28, …? (a) 143 (b) 130 (c) 135 (d) 148
  34. 34.What is the 14th term of the AP 14, 21, 28, 35, …? (a) 91 (b) 98 (c) 105 (d) 112
  35. 35.Which term of the AP 1, 4, 7, 10, … is 22? (a) 7th (b) 10th (c) 8th (d) 9th
  36. 36.Which term of the AP 9, 13, 17, 21, … is 133? (a) 32nd (b) 31st (c) 34th (d) 33rd
  37. 37.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 25 (b) 32 (c) 24 (d) 26
  38. 38.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 47 (b) 300 (c) 600 (d) 324
  39. 39.What is the 30th term of the AP 17, 20, 23, 26, …? (a) 104 (b) 107 (c) 87 (d) 90
  40. 40.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 43 (b) 336 (c) 636 (d) 318

Answer key

  1. 246
  2. 169
  3. 36
  4. 49
  5. 107
  6. 8th
  7. 576
  8. 25
  9. 1653
  10. 64
  11. 154
  12. 325
  13. 24th
  14. 54
  15. 20
  16. 400
  17. 630
  18. 1431
  19. 12th
  20. 139
  21. 91
  22. 68
  23. 81
  24. 11
  25. 1830
  26. 32
  27. 92
  28. 312
  29. 236
  30. 18
  31. 19
  32. 163
  33. 143
  34. 105
  35. 8th
  36. 32nd
  37. 25
  38. 300
  39. 104
  40. 318

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