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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 863 · 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.Which term of the AP 13, 15, 17, 19, … is 59? (a) 23rd (b) 26th (c) 25th (d) 24th
  2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 42 (d) 21
  3. 3.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 30 (b) 28 (c) 38 (d) 29
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 210 (d) 105
  5. 5.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 67 (c) 132 (d) 66
  6. 6.What is the 16th term of the AP 8, 10, 12, 14, …? (a) 30 (b) 40 (c) 32 (d) 38
  7. 7.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 23 (b) 22 (c) 24 (d) 31
  8. 8.Which term of the AP 20, 23, 26, 29, … is 89? (a) 24th (b) 23rd (c) 25th (d) 26th
  9. 9.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 91 (c) 105 (d) 98
  10. 10.Which term of the AP 11, 16, 21, 26, … is 81? (a) 15th (b) 17th (c) 14th (d) 16th
  11. 11.What is the 29th term of the AP 12, 18, 24, 30, …? (a) 186 (b) 174 (c) 168 (d) 180
  12. 12.What is the 33rd term of the AP 1, 6, 11, 16, …? (a) 165 (b) 160 (c) 166 (d) 161
  13. 13.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 703 (c) 722 (d) 741
  14. 14.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 630 (c) 1332 (d) 666
  15. 15.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 14 (b) 16 (c) 17 (d) 15
  16. 16.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 81 (b) 162 (c) 90 (d) 21
  17. 17.What is the 11th term of the AP 3, 7, 11, 15, …? (a) 43 (b) 44 (c) 40 (d) 47
  18. 18.What is the missing term in the AP 20, 27, 34, ?, 48? (a) 41 (b) 40 (c) 42 (d) 48
  19. 19.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 31 (b) 25 (c) 27 (d) 26
  20. 20.What is the missing term in the AP 13, 18, 23, ?, 33? (a) 33 (b) 28 (c) 29 (d) 27
  21. 21.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 60 (b) 14 (c) 120 (d) 61
  22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 39 (d) 210
  23. 23.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 59 (b) 374 (c) 748 (d) 379
  24. 24.What is the 26th term of the AP 11, 13, 15, 17, …? (a) 63 (b) 50 (c) 52 (d) 61
  25. 25.What is the 33rd term of the AP 5, 11, 17, 23, …? (a) 198 (b) 203 (c) 197 (d) 192
  26. 26.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 2775 (c) 5700 (d) 2851
  27. 27.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 15 (b) 16 (c) 17 (d) 23
  28. 28.Which term of the AP 2, 6, 10, 14, … is 98? (a) 27th (b) 25th (c) 26th (d) 24th
  29. 29.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 444 (b) 828 (c) 62 (d) 414
  30. 30.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 29 (b) 30 (c) 31 (d) 36
  31. 31.What is the 13th term of the AP 10, 15, 20, 25, …? (a) 60 (b) 75 (c) 70 (d) 65
  32. 32.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
  33. 33.What is the sum of all the whole numbers from 1 to 79? (a) 3081 (b) 3161 (c) 6320 (d) 3160
  34. 34.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 100 (b) 200 (c) 16 (d) 104
  35. 35.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 20 (b) 17 (c) 18 (d) 19
  36. 36.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 28 (b) 145 (c) 160 (d) 290
  37. 37.What is the 32nd term of the AP 13, 19, 25, 31, …? (a) 199 (b) 205 (c) 192 (d) 186
  38. 38.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 60 (c) 55 (d) 110
  39. 39.What is the missing term in the AP 18, 25, ?, 39, 46? (a) 39 (b) 33 (c) 32 (d) 31
  40. 40.What is the missing term in the AP 13, ?, 19, 22, 25? (a) 19 (b) 17 (c) 15 (d) 16

Answer key

  1. 24th
  2. 36
  3. 29
  4. 196
  5. 66
  6. 38
  7. 23
  8. 24th
  9. 105
  10. 15th
  11. 180
  12. 161
  13. 741
  14. 666
  15. 15
  16. 81
  17. 43
  18. 41
  19. 26
  20. 28
  21. 60
  22. 400
  23. 374
  24. 61
  25. 197
  26. 2850
  27. 16
  28. 25th
  29. 414
  30. 30
  31. 70
  32. 49
  33. 3160
  34. 100
  35. 18
  36. 145
  37. 199
  38. 55
  39. 32
  40. 16

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