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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 915 · 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 7 terms of the AP 6, 7, 8, …? (a) 12 (b) 63 (c) 64 (d) 126
  2. 2.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  3. 3.Which term of the AP 18, 27, 36, 45, … is 126? (a) 13th (b) 12th (c) 14th (d) 15th
  4. 4.What is the 18th term of the AP 20, 22, 24, 26, …? (a) 54 (b) 56 (c) 36 (d) 34
  5. 5.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 22 (b) 21 (c) 24 (d) 23
  6. 6.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 87 (b) 96 (c) 22 (d) 174
  7. 7.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 37 (d) 190
  8. 8.What is the missing term in the AP 7, ?, 15, 19, 23? (a) 11 (b) 15 (c) 12 (d) 10
  9. 9.What is the 16th term of the AP 20, 22, 24, 26, …? (a) 52 (b) 30 (c) 50 (d) 32
  10. 10.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 17 (c) 77 (d) 84
  11. 11.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 59 (d) 930
  12. 12.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 55 (c) 100 (d) 50
  13. 13.What is the 12th term of the AP 4, 9, 14, 19, …? (a) 64 (b) 60 (c) 59 (d) 55
  14. 14.Which term of the AP 10, 18, 26, 34, … is 210? (a) 28th (b) 27th (c) 25th (d) 26th
  15. 15.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 90 (c) 10 (d) 45
  16. 16.What is the 18th term of the AP 20, 26, 32, 38, …? (a) 108 (b) 102 (c) 122 (d) 128
  17. 17.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 462 (b) 69 (c) 429 (d) 858
  18. 18.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 6 (b) 5 (c) 7 (d) 8
  19. 19.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 354 (b) 708 (c) 384 (d) 57
  20. 20.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 105 (c) 91 (d) 98
  21. 21.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 3160 (c) 3240 (d) 6480
  22. 22.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 171 (c) 191 (d) 190
  23. 23.What is the 11th term of the AP 2, 9, 16, 23, …? (a) 70 (b) 72 (c) 77 (d) 79
  24. 24.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 12 (b) 19 (c) 10 (d) 11
  25. 25.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 66 (d) 132
  26. 26.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 80 (c) 43 (d) 40
  27. 27.What is the 21st term of the AP 12, 16, 20, 24, …? (a) 92 (b) 80 (c) 84 (d) 96
  28. 28.What is the 22nd term of the AP 15, 21, 27, 33, …? (a) 126 (b) 141 (c) 147 (d) 132
  29. 29.What is the 18th term of the AP 19, 28, 37, 46, …? (a) 162 (b) 153 (c) 181 (d) 172
  30. 30.What is the 24th term of the AP 19, 22, 25, 28, …? (a) 91 (b) 69 (c) 72 (d) 88
  31. 31.Which term of the AP 1, 9, 17, 25, … is 193? (a) 27th (b) 24th (c) 25th (d) 26th
  32. 32.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  33. 33.Which term of the AP 6, 13, 20, 27, … is 265? (a) 39th (b) 38th (c) 40th (d) 37th
  34. 34.What is the 31st term of the AP 16, 24, 32, 40, …? (a) 248 (b) 264 (c) 240 (d) 256
  35. 35.Which term of the AP 19, 24, 29, 34, … is 124? (a) 23rd (b) 22nd (c) 24th (d) 21st
  36. 36.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 11 (c) 35 (d) 40
  37. 37.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 180 (b) 26 (c) 170 (d) 340
  38. 38.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 37 (b) 133 (c) 266 (d) 154
  39. 39.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 17 (b) 18 (c) 22 (d) 19
  40. 40.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 7310 (c) 3656 (d) 3655

Answer key

  1. 63
  2. 576
  3. 13th
  4. 54
  5. 22
  6. 87
  7. 361
  8. 11
  9. 50
  10. 77
  11. 900
  12. 50
  13. 59
  14. 26th
  15. 45
  16. 122
  17. 429
  18. 6
  19. 354
  20. 105
  21. 3240
  22. 190
  23. 72
  24. 11
  25. 121
  26. 40
  27. 92
  28. 141
  29. 172
  30. 88
  31. 25th
  32. 91
  33. 38th
  34. 256
  35. 22nd
  36. 35
  37. 170
  38. 133
  39. 18
  40. 3655

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