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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 797 · 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 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  2. 2.What is the 19th term of the AP 12, 19, 26, 33, …? (a) 138 (b) 126 (c) 133 (d) 145
  3. 3.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 947 (c) 903 (d) 946
  4. 4.What is the 11th term of the AP 6, 8, 10, 12, …? (a) 28 (b) 22 (c) 20 (d) 26
  5. 5.What is the 29th term of the AP 1, 7, 13, 19, …? (a) 168 (b) 175 (c) 169 (d) 174
  6. 6.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 119 (b) 27 (c) 105 (d) 210
  7. 7.Which term of the AP 17, 26, 35, 44, … is 242? (a) 25th (b) 27th (c) 28th (d) 26th
  8. 8.What is the 14th term of the AP 20, 22, 24, 26, …? (a) 46 (b) 48 (c) 28 (d) 26
  9. 9.What is the 20th term of the AP 12, 16, 20, 24, …? (a) 76 (b) 92 (c) 88 (d) 80
  10. 10.What is the 25th term of the AP 6, 11, 16, 21, …? (a) 120 (b) 131 (c) 126 (d) 125
  11. 11.What is the missing term in the AP 3, 8, 13, ?, 23? (a) 23 (b) 18 (c) 19 (d) 17
  12. 12.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  13. 13.What is the 33rd term of the AP 8, 11, 14, 17, …? (a) 104 (b) 99 (c) 96 (d) 107
  14. 14.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 41 (b) 189 (c) 378 (d) 194
  15. 15.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 378 (c) 756 (d) 351
  16. 16.What is the 28th term of the AP 17, 25, 33, 41, …? (a) 241 (b) 216 (c) 224 (d) 233
  17. 17.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 54 (b) 768 (c) 384 (d) 408
  18. 18.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 506 (c) 253 (d) 242
  19. 19.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 104 (b) 96 (c) 192 (d) 19
  20. 20.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 55 (b) 14 (c) 50 (d) 100
  21. 21.What is the 24th term of the AP 3, 11, 19, 27, …? (a) 192 (b) 187 (c) 184 (d) 195
  22. 22.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 240 (b) 220 (c) 45 (d) 440
  23. 23.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 13 (b) 20 (c) 11 (d) 12
  24. 24.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 69 (b) 864 (c) 432 (d) 468
  25. 25.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 340 (b) 620 (c) 58 (d) 310
  26. 26.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 140 (b) 73 (c) 20 (d) 70
  27. 27.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  28. 28.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 435 (c) 450 (d) 465
  29. 29.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 114 (b) 210 (c) 25 (d) 105
  30. 30.What is the 34th term of the AP 3, 7, 11, 15, …? (a) 135 (b) 139 (c) 132 (d) 136
  31. 31.What is the 28th term of the AP 14, 20, 26, 32, …? (a) 182 (b) 162 (c) 176 (d) 168
  32. 32.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 231 (b) 440 (c) 30 (d) 220
  33. 33.Which term of the AP 7, 11, 15, 19, … is 63? (a) 15th (b) 14th (c) 16th (d) 17th
  34. 34.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 6162 (c) 3003 (d) 3081
  35. 35.What is the 20th term of the AP 16, 21, 26, 31, …? (a) 100 (b) 111 (c) 95 (d) 116
  36. 36.What is the 25th term of the AP 20, 22, 24, 26, …? (a) 70 (b) 48 (c) 50 (d) 68
  37. 37.What is the 12th term of the AP 19, 21, 23, 25, …? (a) 41 (b) 43 (c) 24 (d) 22
  38. 38.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 17 (b) 20 (c) 15 (d) 16
  39. 39.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4608 (c) 4656 (d) 4560
  40. 40.What is the 18th term of the AP 11, 17, 23, 29, …? (a) 108 (b) 119 (c) 102 (d) 113

Answer key

  1. 256
  2. 138
  3. 946
  4. 26
  5. 169
  6. 105
  7. 26th
  8. 46
  9. 88
  10. 126
  11. 18
  12. 841
  13. 104
  14. 189
  15. 378
  16. 233
  17. 384
  18. 253
  19. 96
  20. 50
  21. 187
  22. 220
  23. 12
  24. 432
  25. 310
  26. 70
  27. 121
  28. 465
  29. 105
  30. 135
  31. 176
  32. 220
  33. 15th
  34. 3081
  35. 111
  36. 68
  37. 41
  38. 16
  39. 4656
  40. 113

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