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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 180 · 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 6, 14, 22, 30, … is 174? (a) 21st (b) 24th (c) 22nd (d) 23rd
  2. 2.What is the 25th term of the AP 2, 4, 6, 8, …? (a) 52 (b) 50 (c) 48 (d) 51
  3. 3.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 228 (b) 126 (c) 114 (d) 29
  4. 4.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 342 (d) 324
  5. 5.What is the sum of all the whole numbers from 1 to 73? (a) 5402 (b) 2628 (c) 2702 (d) 2701
  6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 289 (d) 306
  7. 7.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 4 (b) 8 (c) 5 (d) 6
  8. 8.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 180 (b) 26 (c) 90 (d) 100
  9. 9.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 19 (b) 182 (c) 91 (d) 98
  10. 10.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 930 (c) 900 (d) 465
  11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
  12. 12.What is the 20th term of the AP 12, 14, 16, 18, …? (a) 50 (b) 40 (c) 38 (d) 52
  13. 13.What is the 14th term of the AP 18, 22, 26, 30, …? (a) 52 (b) 70 (c) 74 (d) 56
  14. 14.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 792 (b) 66 (c) 429 (d) 396
  15. 15.What is the 34th term of the AP 18, 26, 34, 42, …? (a) 264 (b) 272 (c) 282 (d) 290
  16. 16.Which term of the AP 5, 12, 19, 26, … is 110? (a) 18th (b) 17th (c) 16th (d) 15th
  17. 17.What is the 29th term of the AP 17, 26, 35, 44, …? (a) 269 (b) 252 (c) 278 (d) 261
  18. 18.What is the 20th term of the AP 5, 13, 21, 29, …? (a) 160 (b) 152 (c) 165 (d) 157
  19. 19.Which term of the AP 10, 19, 28, 37, … is 136? (a) 14th (b) 16th (c) 17th (d) 15th
  20. 20.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 8 (c) 40 (d) 36
  21. 21.Which term of the AP 1, 7, 13, 19, … is 73? (a) 15th (b) 13th (c) 14th (d) 12th
  22. 22.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 216 (b) 108 (c) 120 (d) 28
  23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 210 (d) 196
  24. 24.What is the sum of all the whole numbers from 1 to 83? (a) 3486 (b) 6972 (c) 3403 (d) 3487
  25. 25.Which term of the AP 14, 17, 20, 23, … is 104? (a) 31st (b) 32nd (c) 33rd (d) 30th
  26. 26.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 72 (b) 73 (c) 12 (d) 144
  27. 27.Which term of the AP 5, 7, 9, 11, … is 19? (a) 8th (b) 10th (c) 7th (d) 9th
  28. 28.What is the 19th term of the AP 18, 20, 22, 24, …? (a) 38 (b) 54 (c) 56 (d) 36
  29. 29.What is the 27th term of the AP 19, 27, 35, 43, …? (a) 208 (b) 227 (c) 216 (d) 235
  30. 30.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 168 (b) 84 (c) 96 (d) 24
  31. 31.Which term of the AP 13, 17, 21, 25, … is 109? (a) 24th (b) 26th (c) 25th (d) 27th
  32. 32.What is the 21st term of the AP 17, 21, 25, 29, …? (a) 101 (b) 80 (c) 84 (d) 97
  33. 33.What is the 28th term of the AP 19, 24, 29, 34, …? (a) 159 (b) 135 (c) 140 (d) 154
  34. 34.What is the 20th term of the AP 14, 20, 26, 32, …? (a) 114 (b) 120 (c) 134 (d) 128
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  36. 36.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 38 (c) 253 (d) 506
  37. 37.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 64 (b) 15 (c) 128 (d) 72
  38. 38.What is the 23rd term of the AP 12, 16, 20, 24, …? (a) 100 (b) 92 (c) 104 (d) 88
  39. 39.What is the missing term in the AP 14, 19, 24, ?, 34? (a) 29 (b) 28 (c) 30 (d) 34
  40. 40.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 57 (c) 12 (d) 60

Answer key

  1. 22nd
  2. 50
  3. 114
  4. 324
  5. 2701
  6. 289
  7. 5
  8. 90
  9. 91
  10. 900
  11. 49
  12. 50
  13. 70
  14. 396
  15. 282
  16. 16th
  17. 269
  18. 157
  19. 15th
  20. 36
  21. 13th
  22. 108
  23. 196
  24. 3486
  25. 31st
  26. 72
  27. 8th
  28. 54
  29. 227
  30. 84
  31. 25th
  32. 97
  33. 154
  34. 128
  35. 100
  36. 253
  37. 64
  38. 100
  39. 29
  40. 57

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