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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 986 · 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 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 55 (c) 50 (d) 100
  2. 2.What is the 38th term of the AP 9, 14, 19, 24, …? (a) 199 (b) 190 (c) 185 (d) 194
  3. 3.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 10 (b) 7 (c) 9 (d) 8
  4. 4.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  5. 5.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 50 (b) 540 (c) 275 (d) 270
  6. 6.What is the 36th term of the AP 10, 13, 16, 19, …? (a) 118 (b) 115 (c) 105 (d) 108
  7. 7.What is the 37th term of the AP 14, 20, 26, 32, …? (a) 230 (b) 216 (c) 236 (d) 222
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  9. 9.Which term of the AP 20, 26, 32, 38, … is 92? (a) 12th (b) 15th (c) 14th (d) 13th
  10. 10.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 5112 (c) 2557 (d) 2485
  11. 11.What is the 36th term of the AP 17, 21, 25, 29, …? (a) 157 (b) 161 (c) 144 (d) 140
  12. 12.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 80 (b) 14 (c) 43 (d) 40
  13. 13.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 13 (b) 20 (c) 15 (d) 14
  14. 14.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 95 (b) 100 (c) 190 (d) 29
  15. 15.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1540 (c) 1485 (d) 3080
  16. 16.What is the 24th term of the AP 2, 11, 20, 29, …? (a) 216 (b) 207 (c) 209 (d) 218
  17. 17.What is the 21st term of the AP 15, 18, 21, 24, …? (a) 63 (b) 78 (c) 60 (d) 75
  18. 18.What is the 25th term of the AP 3, 12, 21, 30, …? (a) 225 (b) 216 (c) 219 (d) 228
  19. 19.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4754 (c) 4753 (d) 9506
  20. 20.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36
  21. 21.Which term of the AP 6, 12, 18, 24, … is 54? (a) 11th (b) 8th (c) 9th (d) 10th
  22. 22.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 9 (b) 15 (c) 10 (d) 11
  23. 23.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 32 (b) 27 (c) 26 (d) 25
  24. 24.What is the 18th term of the AP 9, 12, 15, 18, …? (a) 54 (b) 60 (c) 51 (d) 63
  25. 25.What is the 11th term of the AP 17, 19, 21, 23, …? (a) 39 (b) 20 (c) 22 (d) 37
  26. 26.What is the 21st term of the AP 7, 13, 19, 25, …? (a) 120 (b) 127 (c) 126 (d) 133
  27. 27.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  28. 28.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  29. 29.What is the 13th term of the AP 15, 21, 27, 33, …? (a) 78 (b) 93 (c) 87 (d) 72
  30. 30.What is the 15th term of the AP 3, 8, 13, 18, …? (a) 70 (b) 75 (c) 78 (d) 73
  31. 31.What is the 20th term of the AP 12, 19, 26, 33, …? (a) 152 (b) 145 (c) 133 (d) 140
  32. 32.Which term of the AP 15, 19, 23, 27, … is 151? (a) 37th (b) 35th (c) 34th (d) 36th
  33. 33.What is the 11th term of the AP 10, 15, 20, 25, …? (a) 50 (b) 60 (c) 65 (d) 55
  34. 34.What is the 24th term of the AP 4, 12, 20, 28, …? (a) 188 (b) 196 (c) 192 (d) 184
  35. 35.Which term of the AP 5, 7, 9, 11, … is 83? (a) 40th (b) 41st (c) 42nd (d) 39th
  36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  37. 37.What is the 16th term of the AP 8, 15, 22, 29, …? (a) 113 (b) 105 (c) 120 (d) 112
  38. 38.What is the missing term in the AP 8, 10, 12, ?, 16? (a) 14 (b) 13 (c) 15 (d) 16
  39. 39.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  40. 40.What is the 31st term of the AP 13, 15, 17, 19, …? (a) 60 (b) 75 (c) 73 (d) 62

Answer key

  1. 50
  2. 194
  3. 8
  4. 169
  5. 270
  6. 115
  7. 230
  8. 25
  9. 13th
  10. 2556
  11. 157
  12. 40
  13. 14
  14. 95
  15. 1540
  16. 209
  17. 75
  18. 219
  19. 4753
  20. 36
  21. 9th
  22. 10
  23. 26
  24. 60
  25. 37
  26. 127
  27. 144
  28. 289
  29. 87
  30. 73
  31. 145
  32. 35th
  33. 60
  34. 188
  35. 40th
  36. 100
  37. 113
  38. 14
  39. 196
  40. 73

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