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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 170 · 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 26th term of the AP 3, 8, 13, 18, …? (a) 128 (b) 125 (c) 133 (d) 130
  2. 2.What is the 38th term of the AP 7, 16, 25, 34, …? (a) 342 (b) 333 (c) 340 (d) 349
  3. 3.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 29 (b) 35 (c) 28 (d) 27
  4. 4.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2888 (c) 5852 (d) 2926
  5. 5.Which term of the AP 20, 25, 30, 35, … is 60? (a) 8th (b) 12th (c) 10th (d) 9th
  6. 6.Which term of the AP 3, 7, 11, 15, … is 111? (a) 27th (b) 28th (c) 29th (d) 30th
  7. 7.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 414 (b) 207 (c) 39 (d) 225
  8. 8.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 11 (b) 90 (c) 46 (d) 45
  9. 9.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 240 (c) 120 (d) 105
  10. 10.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 122 (b) 119 (c) 26 (d) 238
  11. 11.What is the 35th term of the AP 8, 17, 26, 35, …? (a) 306 (b) 323 (c) 315 (d) 314
  12. 12.What is the 15th term of the AP 3, 6, 9, 12, …? (a) 48 (b) 46 (c) 45 (d) 42
  13. 13.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 90 (b) 156 (c) 23 (d) 78
  14. 14.What is the 11th term of the AP 7, 16, 25, 34, …? (a) 106 (b) 90 (c) 99 (d) 97
  15. 15.What is the 23rd term of the AP 17, 24, 31, 38, …? (a) 161 (b) 154 (c) 178 (d) 171
  16. 16.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 2145 (c) 2080 (d) 4290
  17. 17.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 198 (b) 99 (c) 100 (d) 15
  18. 18.What is the 30th term of the AP 19, 22, 25, 28, …? (a) 106 (b) 109 (c) 90 (d) 87
  19. 19.What is the 40th term of the AP 16, 18, 20, 22, …? (a) 96 (b) 78 (c) 80 (d) 94
  20. 20.What is the 16th term of the AP 2, 9, 16, 23, …? (a) 105 (b) 114 (c) 112 (d) 107
  21. 21.Which term of the AP 13, 15, 17, 19, … is 83? (a) 38th (b) 37th (c) 36th (d) 35th
  22. 22.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 277 (c) 253 (d) 276
  23. 23.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 169 (d) 182
  24. 24.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 8930 (c) 4371 (d) 4418
  25. 25.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 432 (b) 29 (c) 216 (d) 228
  26. 26.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 55 (d) 812
  27. 27.What is the 35th term of the AP 6, 10, 14, 18, …? (a) 136 (b) 146 (c) 140 (d) 142
  28. 28.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 47 (d) 300
  29. 29.Which term of the AP 19, 28, 37, 46, … is 127? (a) 14th (b) 15th (c) 13th (d) 12th
  30. 30.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 315 (b) 340 (c) 630 (d) 54
  31. 31.What is the 13th term of the AP 17, 19, 21, 23, …? (a) 26 (b) 24 (c) 41 (d) 43
  32. 32.What is the 34th term of the AP 12, 17, 22, 27, …? (a) 165 (b) 182 (c) 170 (d) 177
  33. 33.Which term of the AP 6, 9, 12, 15, … is 123? (a) 41st (b) 40th (c) 42nd (d) 39th
  34. 34.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2702 (c) 5402 (d) 2701
  35. 35.Which term of the AP 20, 27, 34, 41, … is 146? (a) 18th (b) 19th (c) 20th (d) 21st
  36. 36.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 91 (c) 78 (d) 92
  37. 37.What is the 12th term of the AP 17, 19, 21, 23, …? (a) 39 (b) 22 (c) 41 (d) 24
  38. 38.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 4951 (c) 9900 (d) 4950
  39. 39.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 50 (c) 110 (d) 55
  40. 40.What is the 31st term of the AP 16, 24, 32, 40, …? (a) 264 (b) 256 (c) 248 (d) 240

Answer key

  1. 128
  2. 340
  3. 28
  4. 2926
  5. 9th
  6. 28th
  7. 207
  8. 45
  9. 120
  10. 119
  11. 314
  12. 45
  13. 78
  14. 97
  15. 171
  16. 2145
  17. 99
  18. 106
  19. 94
  20. 107
  21. 36th
  22. 276
  23. 169
  24. 4465
  25. 216
  26. 784
  27. 142
  28. 576
  29. 13th
  30. 315
  31. 41
  32. 177
  33. 40th
  34. 2701
  35. 19th
  36. 91
  37. 39
  38. 4950
  39. 55
  40. 256

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