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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 590 · 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 5 terms of the AP 6, 9, 12, …? (a) 63 (b) 60 (c) 120 (d) 18
  2. 2.What is the 38th term of the AP 16, 21, 26, 31, …? (a) 185 (b) 190 (c) 201 (d) 206
  3. 3.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  5. 5.What is the 24th term of the AP 6, 13, 20, 27, …? (a) 174 (b) 161 (c) 168 (d) 167
  6. 6.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 55 (c) 60 (d) 110
  7. 7.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 40 (b) 48 (c) 38 (d) 39
  8. 8.What is the 18th term of the AP 10, 13, 16, 19, …? (a) 61 (b) 64 (c) 54 (d) 51
  9. 9.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 21 (b) 168 (c) 84 (d) 87
  10. 10.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 252 (b) 27 (c) 129 (d) 126
  11. 11.What is the 15th term of the AP 20, 23, 26, 29, …? (a) 42 (b) 45 (c) 65 (d) 62
  12. 12.Which term of the AP 11, 19, 27, 35, … is 155? (a) 21st (b) 18th (c) 20th (d) 19th
  13. 13.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 280 (b) 152 (c) 28 (d) 140
  14. 14.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 192 (b) 114 (c) 31 (d) 96
  15. 15.Which term of the AP 4, 13, 22, 31, … is 193? (a) 24th (b) 23rd (c) 22nd (d) 21st
  16. 16.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 900 (c) 930 (d) 59
  17. 17.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 70 (c) 11 (d) 35
  18. 18.Which term of the AP 18, 21, 24, 27, … is 123? (a) 41st (b) 37th (c) 36th (d) 35th
  19. 19.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 95 (b) 90 (c) 28 (d) 180
  20. 20.Which term of the AP 11, 16, 21, 26, … is 206? (a) 39th (b) 42nd (c) 41st (d) 40th
  21. 21.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 33 (b) 210 (c) 120 (d) 105
  22. 22.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 816 (b) 408 (c) 67 (d) 444
  23. 23.What is the 23rd term of the AP 17, 20, 23, 26, …? (a) 83 (b) 69 (c) 66 (d) 86
  24. 24.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 11 (b) 64 (c) 63 (d) 126
  25. 25.Which term of the AP 14, 18, 22, 26, … is 126? (a) 28th (b) 30th (c) 31st (d) 29th
  26. 26.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  27. 27.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 35 (b) 26 (c) 25 (d) 27
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 42 (d) 21
  29. 29.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 56 (c) 682 (d) 341
  30. 30.What is the 14th term of the AP 10, 13, 16, 19, …? (a) 42 (b) 49 (c) 39 (d) 52
  31. 31.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 152 (b) 33 (c) 168 (d) 304
  32. 32.What is the 11th term of the AP 19, 24, 29, 34, …? (a) 55 (b) 74 (c) 50 (d) 69
  33. 33.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1378 (c) 1432 (d) 1431
  34. 34.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 78 (b) 92 (c) 81 (d) 89
  35. 35.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 325 (d) 625
  36. 36.What is the 12th term of the AP 1, 3, 5, 7, …? (a) 24 (b) 23 (c) 22 (d) 25
  37. 37.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2557 (c) 2485 (d) 2556
  38. 38.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 7 (b) 5 (c) 8 (d) 6
  39. 39.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 55 (c) 67 (d) 132
  40. 40.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1378 (c) 2756 (d) 1352

Answer key

  1. 60
  2. 201
  3. 144
  4. 100
  5. 167
  6. 55
  7. 39
  8. 61
  9. 84
  10. 126
  11. 62
  12. 19th
  13. 140
  14. 96
  15. 22nd
  16. 900
  17. 35
  18. 36th
  19. 90
  20. 40th
  21. 105
  22. 408
  23. 83
  24. 63
  25. 29th
  26. 169
  27. 26
  28. 36
  29. 341
  30. 49
  31. 152
  32. 69
  33. 1431
  34. 89
  35. 625
  36. 23
  37. 2556
  38. 6
  39. 66
  40. 1378

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