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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 755 · 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 12 terms of the AP 1, 2, 3, …? (a) 84 (b) 78 (c) 156 (d) 12
  2. 2.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 252 (b) 36 (c) 468 (d) 234
  3. 3.Which term of the AP 19, 21, 23, 25, … is 73? (a) 27th (b) 28th (c) 29th (d) 30th
  4. 4.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 32 (b) 144 (c) 160 (d) 288
  5. 5.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 120 (c) 29 (d) 240
  6. 6.What is the 21st term of the AP 12, 19, 26, 33, …? (a) 159 (b) 140 (c) 152 (d) 147
  7. 7.What is the 37th term of the AP 9, 13, 17, 21, …? (a) 157 (b) 153 (c) 144 (d) 148
  8. 8.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 16 (b) 15 (c) 20 (d) 17
  9. 9.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 324 (d) 35
  10. 10.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 13 (b) 15 (c) 20 (d) 14
  11. 11.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 378 (b) 59 (c) 756 (d) 408
  12. 12.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 150 (b) 80 (c) 75 (d) 12
  13. 13.What is the 28th term of the AP 13, 22, 31, 40, …? (a) 243 (b) 256 (c) 252 (d) 265
  14. 14.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 456 (b) 840 (c) 420 (d) 68
  15. 15.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 21 (b) 150 (c) 75 (d) 78
  16. 16.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  17. 17.What is the missing term in the AP 15, ?, 19, 21, 23? (a) 19 (b) 16 (c) 18 (d) 17
  18. 18.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 21 (b) 20 (c) 19 (d) 23
  19. 19.Which term of the AP 20, 28, 36, 44, … is 124? (a) 14th (b) 16th (c) 15th (d) 13th
  20. 20.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 21 (d) 42
  21. 21.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 25 (b) 80 (c) 130 (d) 65
  22. 22.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 13 (b) 12 (c) 17 (d) 11
  23. 23.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4095 (c) 4186 (d) 4187
  24. 24.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210
  25. 25.What is the 19th term of the AP 4, 8, 12, 16, …? (a) 77 (b) 76 (c) 80 (d) 72
  26. 26.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 35 (b) 25 (c) 27 (d) 26
  27. 27.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 182 (c) 22 (d) 94
  28. 28.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 264 (b) 504 (c) 252 (d) 32
  29. 29.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 78 (c) 12 (d) 77
  30. 30.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 9 (b) 46 (c) 90 (d) 45
  31. 31.Which term of the AP 20, 29, 38, 47, … is 119? (a) 13th (b) 11th (c) 12th (d) 14th
  32. 32.Which term of the AP 8, 16, 24, 32, … is 192? (a) 25th (b) 23rd (c) 26th (d) 24th
  33. 33.What is the 40th term of the AP 11, 14, 17, 20, …? (a) 128 (b) 117 (c) 120 (d) 131
  34. 34.What is the 38th term of the AP 12, 19, 26, 33, …? (a) 278 (b) 271 (c) 259 (d) 266
  35. 35.What is the 12th term of the AP 7, 14, 21, 28, …? (a) 91 (b) 85 (c) 77 (d) 84
  36. 36.What is the 23rd term of the AP 9, 13, 17, 21, …? (a) 101 (b) 88 (c) 92 (d) 97
  37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 49 (d) 13
  38. 38.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 17 (b) 16 (c) 21 (d) 18
  39. 39.What is the 32nd term of the AP 15, 21, 27, 33, …? (a) 192 (b) 207 (c) 201 (d) 186
  40. 40.What is the 19th term of the AP 5, 13, 21, 29, …? (a) 152 (b) 149 (c) 144 (d) 157

Answer key

  1. 78
  2. 234
  3. 28th
  4. 144
  5. 225
  6. 152
  7. 153
  8. 16
  9. 324
  10. 14
  11. 378
  12. 75
  13. 256
  14. 420
  15. 75
  16. 25
  17. 17
  18. 20
  19. 14th
  20. 36
  21. 65
  22. 12
  23. 4186
  24. 196
  25. 76
  26. 26
  27. 91
  28. 252
  29. 77
  30. 45
  31. 12th
  32. 24th
  33. 128
  34. 271
  35. 84
  36. 97
  37. 49
  38. 17
  39. 201
  40. 149

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