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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 440 · 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 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 529 (c) 552 (d) 45
  2. 2.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  3. 3.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 53 (b) 45 (c) 44 (d) 43
  4. 4.What is the 26th term of the AP 7, 11, 15, 19, …? (a) 111 (b) 100 (c) 107 (d) 104
  5. 5.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 703 (c) 1406 (d) 704
  6. 6.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 210 (b) 37 (c) 380 (d) 190
  7. 7.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 150 (b) 80 (c) 75 (d) 25
  8. 8.Which term of the AP 7, 11, 15, 19, … is 43? (a) 11th (b) 9th (c) 12th (d) 10th
  9. 9.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  10. 10.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  11. 11.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 96 (b) 162 (c) 26 (d) 81
  12. 12.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 115 (b) 32 (c) 200 (d) 100
  13. 13.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 228 (b) 30 (c) 240 (d) 456
  14. 14.What is the 15th term of the AP 15, 22, 29, 36, …? (a) 113 (b) 98 (c) 105 (d) 120
  15. 15.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 96 (b) 22 (c) 174 (d) 87
  16. 16.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 150 (b) 23 (c) 140 (d) 280
  17. 17.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 84 (b) 48 (c) 42 (d) 12
  18. 18.What is the 31st term of the AP 18, 20, 22, 24, …? (a) 78 (b) 60 (c) 80 (d) 62
  19. 19.What is the 28th term of the AP 13, 20, 27, 34, …? (a) 209 (b) 202 (c) 189 (d) 196
  20. 20.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 444 (b) 414 (c) 828 (d) 62
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 66 (d) 21
  22. 22.What is the missing term in the AP 5, ?, 21, 29, 37? (a) 13 (b) 21 (c) 14 (d) 12
  23. 23.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 185 (b) 200 (c) 32 (d) 370
  24. 24.Which term of the AP 17, 26, 35, 44, … is 296? (a) 31st (b) 32nd (c) 33rd (d) 34th
  25. 25.What is the 25th term of the AP 11, 19, 27, 35, …? (a) 192 (b) 200 (c) 211 (d) 203
  26. 26.What is the 36th term of the AP 7, 10, 13, 16, …? (a) 115 (b) 105 (c) 108 (d) 112
  27. 27.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 37 (b) 38 (c) 46 (d) 39
  28. 28.What is the 21st term of the AP 17, 20, 23, 26, …? (a) 80 (b) 60 (c) 77 (d) 63
  29. 29.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 6 (b) 8 (c) 11 (d) 7
  30. 30.What is the missing term in the AP 11, 17, ?, 29, 35? (a) 23 (b) 29 (c) 24 (d) 22
  31. 31.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  32. 32.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 23 (b) 78 (c) 90 (d) 156
  33. 33.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 33 (b) 41 (c) 31 (d) 32
  34. 34.What is the 10th term of the AP 20, 25, 30, 35, …? (a) 65 (b) 70 (c) 45 (d) 50
  35. 35.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 29 (b) 24 (c) 22 (d) 23
  36. 36.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 160 (b) 26 (c) 80 (d) 85
  37. 37.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 210 (d) 400
  38. 38.What is the 36th term of the AP 20, 25, 30, 35, …? (a) 175 (b) 195 (c) 180 (d) 200
  39. 39.Which term of the AP 4, 6, 8, 10, … is 26? (a) 12th (b) 11th (c) 14th (d) 13th
  40. 40.Which term of the AP 2, 11, 20, 29, … is 344? (a) 38th (b) 40th (c) 41st (d) 39th

Answer key

  1. 529
  2. 324
  3. 44
  4. 107
  5. 703
  6. 190
  7. 75
  8. 10th
  9. 49
  10. 625
  11. 81
  12. 100
  13. 228
  14. 113
  15. 87
  16. 140
  17. 42
  18. 78
  19. 202
  20. 414
  21. 121
  22. 13
  23. 185
  24. 32nd
  25. 203
  26. 112
  27. 38
  28. 77
  29. 7
  30. 23
  31. 361
  32. 78
  33. 32
  34. 65
  35. 23
  36. 80
  37. 400
  38. 195
  39. 12th
  40. 39th

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