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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 540 · 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 missing term in the AP 5, 9, ?, 17, 21? (a) 17 (b) 12 (c) 13 (d) 14
  2. 2.What is the 16th term of the AP 18, 22, 26, 30, …? (a) 64 (b) 82 (c) 78 (d) 60
  3. 3.What is the missing term in the AP 2, 9, 16, ?, 30? (a) 30 (b) 23 (c) 24 (d) 22
  4. 4.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 703 (c) 704 (d) 666
  5. 5.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3042 (c) 6162 (d) 3003
  6. 6.What is the 12th term of the AP 2, 4, 6, 8, …? (a) 25 (b) 24 (c) 22 (d) 26
  7. 7.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 336 (b) 35 (c) 184 (d) 168
  8. 8.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 90 (b) 180 (c) 95 (d) 28
  9. 9.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 170 (b) 85 (c) 90 (d) 13
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  11. 11.What is the 17th term of the AP 15, 21, 27, 33, …? (a) 111 (b) 96 (c) 102 (d) 117
  12. 12.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 15 (b) 70 (c) 63 (d) 126
  13. 13.What is the 18th term of the AP 6, 9, 12, 15, …? (a) 60 (b) 51 (c) 57 (d) 54
  14. 14.What is the 16th term of the AP 15, 17, 19, 21, …? (a) 45 (b) 47 (c) 32 (d) 30
  15. 15.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 946 (c) 990 (d) 968
  16. 16.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 14 (b) 100 (c) 99 (d) 198
  17. 17.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 252 (b) 126 (c) 129 (d) 26
  18. 18.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 630 (c) 1332 (d) 666
  19. 19.What is the sum of all the whole numbers from 1 to 20? (a) 190 (b) 200 (c) 210 (d) 420
  20. 20.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 27 (b) 26 (c) 28 (d) 32
  21. 21.What is the 30th term of the AP 14, 17, 20, 23, …? (a) 87 (b) 90 (c) 101 (d) 104
  22. 22.What is the 17th term of the AP 13, 21, 29, 37, …? (a) 141 (b) 128 (c) 149 (d) 136
  23. 23.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 2970 (c) 1431 (d) 1485
  24. 24.What is the 24th term of the AP 5, 11, 17, 23, …? (a) 144 (b) 143 (c) 149 (d) 138
  25. 25.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 150 (b) 140 (c) 280 (d) 23
  26. 26.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 2146 (c) 4290 (d) 2145
  27. 27.Which term of the AP 13, 17, 21, 25, … is 73? (a) 18th (b) 17th (c) 16th (d) 15th
  28. 28.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 210 (c) 114 (d) 105
  29. 29.What is the 30th term of the AP 9, 16, 23, 30, …? (a) 210 (b) 203 (c) 212 (d) 219
  30. 30.What is the 38th term of the AP 17, 20, 23, 26, …? (a) 128 (b) 114 (c) 131 (d) 111
  31. 31.What is the 29th term of the AP 6, 12, 18, 24, …? (a) 168 (b) 180 (c) 175 (d) 174
  32. 32.Which term of the AP 2, 10, 18, 26, … is 194? (a) 27th (b) 24th (c) 26th (d) 25th
  33. 33.What is the 25th term of the AP 4, 8, 12, 16, …? (a) 104 (b) 100 (c) 101 (d) 96
  34. 34.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 28 (c) 186 (d) 93
  35. 35.Which term of the AP 10, 16, 22, 28, … is 184? (a) 29th (b) 32nd (c) 31st (d) 30th
  36. 36.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 528 (c) 562 (d) 561
  37. 37.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 12 (b) 154 (c) 77 (d) 78
  38. 38.What is the 27th term of the AP 14, 17, 20, 23, …? (a) 92 (b) 78 (c) 81 (d) 95
  39. 39.What is the 19th term of the AP 11, 17, 23, 29, …? (a) 114 (b) 108 (c) 125 (d) 119
  40. 40.Which term of the AP 18, 20, 22, 24, … is 62? (a) 22nd (b) 24th (c) 31st (d) 23rd

Answer key

  1. 13
  2. 78
  3. 23
  4. 703
  5. 3081
  6. 24
  7. 168
  8. 90
  9. 85
  10. 676
  11. 111
  12. 63
  13. 57
  14. 45
  15. 990
  16. 99
  17. 126
  18. 666
  19. 210
  20. 27
  21. 101
  22. 141
  23. 1485
  24. 143
  25. 140
  26. 2145
  27. 16th
  28. 105
  29. 212
  30. 128
  31. 174
  32. 25th
  33. 100
  34. 93
  35. 30th
  36. 561
  37. 77
  38. 92
  39. 119
  40. 23rd

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