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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 344 · 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 25th term of the AP 14, 16, 18, 20, …? (a) 48 (b) 50 (c) 62 (d) 64
  2. 2.What is the 17th term of the AP 17, 21, 25, 29, …? (a) 64 (b) 68 (c) 85 (d) 81
  3. 3.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 6162 (c) 3042 (d) 3003
  4. 4.What is the 33rd term of the AP 6, 12, 18, 24, …? (a) 204 (b) 192 (c) 198 (d) 199
  5. 5.What is the missing term in the AP 16, 25, 34, ?, 52? (a) 44 (b) 52 (c) 43 (d) 42
  6. 6.What is the 18th term of the AP 9, 16, 23, 30, …? (a) 126 (b) 135 (c) 119 (d) 128
  7. 7.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 112 (b) 20 (c) 208 (d) 104
  8. 8.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 17 (b) 21 (c) 18 (d) 19
  9. 9.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 95 (b) 180 (c) 90 (d) 28
  10. 10.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 31 (b) 39 (c) 29 (d) 30
  11. 11.Which term of the AP 3, 7, 11, 15, … is 71? (a) 17th (b) 18th (c) 19th (d) 20th
  12. 12.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 18 (b) 23 (c) 20 (d) 19
  13. 13.What is the 17th term of the AP 20, 22, 24, 26, …? (a) 32 (b) 52 (c) 34 (d) 54
  14. 14.What is the missing term in the AP 20, 27, ?, 41, 48? (a) 33 (b) 35 (c) 41 (d) 34
  15. 15.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 600 (d) 576
  16. 16.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 10100 (d) 5000
  17. 17.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 26 (b) 24 (c) 25 (d) 32
  18. 18.What is the 10th term of the AP 13, 22, 31, 40, …? (a) 103 (b) 81 (c) 90 (d) 94
  19. 19.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 12 (b) 16 (c) 10 (d) 11
  20. 20.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 132 (b) 34 (c) 228 (d) 114
  21. 21.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 968 (c) 1980 (d) 990
  22. 22.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 6320 (c) 3161 (d) 3081
  23. 23.What is the 26th term of the AP 16, 25, 34, 43, …? (a) 234 (b) 250 (c) 241 (d) 225
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 100 (d) 55
  25. 25.Which term of the AP 7, 9, 11, 13, … is 53? (a) 23rd (b) 25th (c) 26th (d) 24th
  26. 26.What is the sum of all the whole numbers from 1 to 68? (a) 2346 (b) 2312 (c) 4692 (d) 2278
  27. 27.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 676 (d) 702
  28. 28.Which term of the AP 10, 13, 16, 19, … is 76? (a) 25th (b) 22nd (c) 24th (d) 23rd
  29. 29.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 14 (b) 13 (c) 12 (d) 15
  30. 30.What is the 36th term of the AP 18, 22, 26, 30, …? (a) 162 (b) 140 (c) 144 (d) 158
  31. 31.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3003 (c) 3004 (d) 2926
  32. 32.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 324 (b) 42 (c) 306 (d) 612
  33. 33.What is the missing term in the AP 5, 14, ?, 32, 41? (a) 22 (b) 32 (c) 24 (d) 23
  34. 34.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 70 (b) 130 (c) 23 (d) 65
  35. 35.What is the 21st term of the AP 7, 13, 19, 25, …? (a) 133 (b) 126 (c) 127 (d) 120
  36. 36.What is the 27th term of the AP 19, 26, 33, 40, …? (a) 201 (b) 182 (c) 189 (d) 208
  37. 37.What is the 33rd term of the AP 6, 10, 14, 18, …? (a) 138 (b) 132 (c) 128 (d) 134
  38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 462 (d) 231
  39. 39.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 154 (b) 78 (c) 14 (d) 77
  40. 40.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 852 (b) 456 (c) 426 (d) 63

Answer key

  1. 62
  2. 81
  3. 3081
  4. 198
  5. 43
  6. 128
  7. 104
  8. 18
  9. 90
  10. 30
  11. 18th
  12. 19
  13. 52
  14. 34
  15. 576
  16. 5050
  17. 25
  18. 94
  19. 11
  20. 114
  21. 990
  22. 3160
  23. 241
  24. 100
  25. 24th
  26. 2346
  27. 676
  28. 23rd
  29. 13
  30. 158
  31. 3003
  32. 306
  33. 23
  34. 65
  35. 127
  36. 201
  37. 134
  38. 441
  39. 77
  40. 426

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