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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 17 · 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 4, 8, 12, …? (a) 312 (b) 48 (c) 624 (d) 336
  2. 2.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 102 (c) 120 (d) 204
  3. 3.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 66 (c) 36 (d) 33
  4. 4.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 72 (c) 156 (d) 66
  5. 5.What is the 36th term of the AP 16, 22, 28, 34, …? (a) 216 (b) 232 (c) 226 (d) 210
  6. 6.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 43 (b) 34 (c) 33 (d) 35
  7. 7.What is the 31st term of the AP 10, 18, 26, 34, …? (a) 240 (b) 258 (c) 250 (d) 248
  8. 8.What is the 26th term of the AP 6, 9, 12, 15, …? (a) 75 (b) 84 (c) 81 (d) 78
  9. 9.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4371 (c) 4372 (d) 4278
  10. 10.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 406 (c) 392 (d) 812
  11. 11.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 420 (b) 210 (c) 228 (d) 34
  12. 12.What is the 26th term of the AP 1, 9, 17, 25, …? (a) 209 (b) 201 (c) 208 (d) 200
  13. 13.What is the 33rd term of the AP 8, 14, 20, 26, …? (a) 200 (b) 198 (c) 192 (d) 206
  14. 14.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 272 (c) 136 (d) 128
  15. 15.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 4290 (c) 2145 (d) 2080
  16. 16.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 65 (b) 55 (c) 110 (d) 19
  17. 17.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 3160 (c) 3200 (d) 6480
  18. 18.What is the 14th term of the AP 3, 12, 21, 30, …? (a) 129 (b) 117 (c) 120 (d) 126
  19. 19.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 19 (b) 18 (c) 17 (d) 20
  20. 20.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 162 (b) 165 (c) 324 (d) 30
  21. 21.Which term of the AP 6, 13, 20, 27, … is 272? (a) 38th (b) 40th (c) 39th (d) 41st
  22. 22.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 12 (b) 16 (c) 14 (d) 13
  23. 23.What is the 18th term of the AP 5, 10, 15, 20, …? (a) 91 (b) 90 (c) 85 (d) 95
  24. 24.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 30 (b) 29 (c) 31 (d) 34
  25. 25.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 204 (b) 27 (c) 114 (d) 102
  26. 26.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 221 (b) 432 (c) 44 (d) 216
  27. 27.Which term of the AP 11, 14, 17, 20, … is 44? (a) 14th (b) 12th (c) 13th (d) 11th
  28. 28.What is the 13th term of the AP 10, 16, 22, 28, …? (a) 78 (b) 82 (c) 88 (d) 72
  29. 29.Which term of the AP 3, 9, 15, 21, … is 57? (a) 9th (b) 12th (c) 10th (d) 11th
  30. 30.What is the 25th term of the AP 8, 10, 12, 14, …? (a) 50 (b) 58 (c) 56 (d) 48
  31. 31.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 272 (d) 31
  32. 32.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 16 (b) 20 (c) 15 (d) 17
  33. 33.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 17 (d) 81
  34. 34.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3828 (c) 7656 (d) 3829
  35. 35.Which term of the AP 17, 24, 31, 38, … is 220? (a) 32nd (b) 29th (c) 30th (d) 31st
  36. 36.What is the 17th term of the AP 2, 6, 10, 14, …? (a) 68 (b) 70 (c) 66 (d) 64
  37. 37.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
  38. 38.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 18 (b) 16 (c) 15 (d) 14
  39. 39.What is the missing term in the AP 16, ?, 28, 34, 40? (a) 23 (b) 28 (c) 22 (d) 21
  40. 40.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 400 (b) 46 (c) 224 (d) 200

Answer key

  1. 312
  2. 102
  3. 33
  4. 78
  5. 226
  6. 34
  7. 250
  8. 81
  9. 4371
  10. 406
  11. 210
  12. 201
  13. 200
  14. 136
  15. 2145
  16. 55
  17. 3240
  18. 120
  19. 18
  20. 162
  21. 39th
  22. 13
  23. 90
  24. 30
  25. 102
  26. 216
  27. 12th
  28. 82
  29. 10th
  30. 56
  31. 256
  32. 16
  33. 81
  34. 3828
  35. 30th
  36. 66
  37. 36
  38. 15
  39. 22
  40. 200

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