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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 421 · 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 24th term of the AP 14, 20, 26, 32, …? (a) 138 (b) 152 (c) 144 (d) 158
  2. 2.What is the 13th term of the AP 8, 10, 12, 14, …? (a) 34 (b) 26 (c) 24 (d) 32
  3. 3.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 135 (b) 140 (c) 270 (d) 18
  4. 4.What is the 12th term of the AP 12, 16, 20, 24, …? (a) 60 (b) 56 (c) 44 (d) 48
  5. 5.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 46 (b) 38 (c) 40 (d) 39
  6. 6.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 72 (c) 36 (d) 11
  7. 7.Which term of the AP 5, 8, 11, 14, … is 32? (a) 12th (b) 11th (c) 9th (d) 10th
  8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
  9. 9.Which term of the AP 10, 17, 24, 31, … is 227? (a) 31st (b) 34th (c) 33rd (d) 32nd
  10. 10.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 22 (b) 23 (c) 25 (d) 24
  11. 11.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 350 (b) 700 (c) 380 (d) 62
  12. 12.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 820 (c) 780 (d) 1640
  13. 13.What is the 31st term of the AP 10, 16, 22, 28, …? (a) 190 (b) 180 (c) 196 (d) 186
  14. 14.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 55 (c) 110 (d) 45
  15. 15.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 43 (b) 53 (c) 45 (d) 44
  16. 16.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 12 (b) 60 (c) 57 (d) 114
  17. 17.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 7 (b) 9 (c) 8 (d) 11
  18. 18.What is the missing term in the AP 14, ?, 32, 41, 50? (a) 23 (b) 24 (c) 22 (d) 32
  19. 19.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 160 (b) 85 (c) 26 (d) 80
  20. 20.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 100 (b) 50 (c) 53 (d) 16
  21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  22. 22.Which term of the AP 5, 14, 23, 32, … is 167? (a) 21st (b) 20th (c) 19th (d) 18th
  23. 23.What is the missing term in the AP 10, ?, 18, 22, 26? (a) 13 (b) 15 (c) 14 (d) 18
  24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 420 (d) 210
  25. 25.Which term of the AP 16, 20, 24, 28, … is 172? (a) 41st (b) 40th (c) 39th (d) 43rd
  26. 26.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 21 (b) 15 (c) 14 (d) 16
  27. 27.Which term of the AP 16, 21, 26, 31, … is 211? (a) 39th (b) 40th (c) 41st (d) 42nd
  28. 28.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 1056 (c) 528 (d) 512
  29. 29.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 81 (b) 162 (c) 21 (d) 90
  30. 30.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 54 (b) 10 (c) 55 (d) 108
  31. 31.What is the 24th term of the AP 4, 10, 16, 22, …? (a) 148 (b) 138 (c) 142 (d) 144
  32. 32.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 240 (b) 22 (c) 120 (d) 128
  33. 33.What is the 29th term of the AP 1, 7, 13, 19, …? (a) 168 (b) 174 (c) 169 (d) 175
  34. 34.What is the 12th term of the AP 19, 25, 31, 37, …? (a) 72 (b) 91 (c) 66 (d) 85
  35. 35.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 40 (b) 220 (c) 440 (d) 240
  36. 36.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 21 (c) 6 (d) 40
  37. 37.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 562 (c) 528 (d) 1122
  38. 38.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 225 (c) 450 (d) 243
  39. 39.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 294 (b) 152 (c) 36 (d) 147
  40. 40.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 12 (b) 78 (c) 154 (d) 77

Answer key

  1. 152
  2. 32
  3. 135
  4. 56
  5. 39
  6. 36
  7. 10th
  8. 36
  9. 32nd
  10. 23
  11. 350
  12. 820
  13. 190
  14. 55
  15. 44
  16. 57
  17. 8
  18. 23
  19. 80
  20. 50
  21. 25
  22. 19th
  23. 14
  24. 400
  25. 40th
  26. 15
  27. 40th
  28. 528
  29. 81
  30. 54
  31. 142
  32. 120
  33. 169
  34. 85
  35. 220
  36. 20
  37. 561
  38. 225
  39. 147
  40. 77

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