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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 411 · 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 2, 5, 8, 11, … is 107? (a) 35th (b) 37th (c) 38th (d) 36th
  2. 2.What is the 22nd term of the AP 10, 16, 22, 28, …? (a) 142 (b) 132 (c) 136 (d) 126
  3. 3.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 105 (c) 210 (d) 91
  4. 4.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 22 (b) 17 (c) 18 (d) 19
  5. 5.What is the 19th term of the AP 10, 15, 20, 25, …? (a) 105 (b) 95 (c) 90 (d) 100
  6. 6.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 3782 (c) 1892 (d) 1891
  7. 7.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 340 (b) 26 (c) 180 (d) 170
  8. 8.What is the 24th term of the AP 5, 9, 13, 17, …? (a) 101 (b) 97 (c) 96 (d) 92
  9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 169 (d) 182
  10. 10.Which term of the AP 6, 14, 22, 30, … is 110? (a) 16th (b) 15th (c) 13th (d) 14th
  11. 11.What is the sum of all the whole numbers from 1 to 58? (a) 1711 (b) 1682 (c) 1653 (d) 3422
  12. 12.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 7 (b) 8 (c) 9 (d) 11
  13. 13.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 95 (b) 25 (c) 170 (d) 85
  14. 14.What is the 32nd term of the AP 6, 9, 12, 15, …? (a) 96 (b) 93 (c) 99 (d) 102
  15. 15.Which term of the AP 10, 14, 18, 22, … is 134? (a) 33rd (b) 31st (c) 32nd (d) 34th
  16. 16.What is the 25th term of the AP 16, 20, 24, 28, …? (a) 100 (b) 116 (c) 96 (d) 112
  17. 17.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 6642 (c) 3322 (d) 3240
  18. 18.What is the sum of all the whole numbers from 1 to 79? (a) 3081 (b) 6320 (c) 3160 (d) 3161
  19. 19.What is the 18th term of the AP 19, 26, 33, 40, …? (a) 145 (b) 138 (c) 126 (d) 119
  20. 20.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 326 (c) 650 (d) 325
  21. 21.Which term of the AP 17, 25, 33, 41, … is 185? (a) 24th (b) 22nd (c) 23rd (d) 21st
  22. 22.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 36 (b) 34 (c) 35 (d) 43
  23. 23.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
  24. 24.Which term of the AP 17, 20, 23, 26, … is 74? (a) 21st (b) 22nd (c) 19th (d) 20th
  25. 25.What is the 11th term of the AP 8, 13, 18, 23, …? (a) 50 (b) 55 (c) 63 (d) 58
  26. 26.What is the 30th term of the AP 18, 21, 24, 27, …? (a) 90 (b) 108 (c) 87 (d) 105
  27. 27.What is the 33rd term of the AP 2, 6, 10, 14, …? (a) 134 (b) 130 (c) 132 (d) 128
  28. 28.What is the 32nd term of the AP 18, 26, 34, 42, …? (a) 256 (b) 248 (c) 266 (d) 274
  29. 29.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 19 (b) 27 (c) 21 (d) 20
  30. 30.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 109 (b) 16 (c) 108 (d) 216
  31. 31.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 117 (b) 20 (c) 216 (d) 108
  32. 32.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1596 (c) 1568 (d) 3192
  33. 33.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 8 (c) 36 (d) 40
  34. 34.What is the 27th term of the AP 19, 28, 37, 46, …? (a) 262 (b) 234 (c) 253 (d) 243
  35. 35.What is the 21st term of the AP 20, 29, 38, 47, …? (a) 189 (b) 200 (c) 180 (d) 209
  36. 36.Which term of the AP 5, 11, 17, 23, … is 71? (a) 13th (b) 11th (c) 12th (d) 14th
  37. 37.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 14 (b) 22 (c) 16 (d) 15
  38. 38.What is the 18th term of the AP 17, 26, 35, 44, …? (a) 179 (b) 153 (c) 162 (d) 170
  39. 39.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 35 (b) 336 (c) 184 (d) 168
  40. 40.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 108 (b) 216 (c) 33 (d) 126

Answer key

  1. 36th
  2. 136
  3. 105
  4. 18
  5. 100
  6. 1891
  7. 170
  8. 97
  9. 169
  10. 14th
  11. 1711
  12. 8
  13. 85
  14. 99
  15. 32nd
  16. 112
  17. 3321
  18. 3160
  19. 138
  20. 325
  21. 22nd
  22. 35
  23. 841
  24. 20th
  25. 58
  26. 105
  27. 130
  28. 266
  29. 20
  30. 108
  31. 108
  32. 1596
  33. 36
  34. 253
  35. 200
  36. 12th
  37. 15
  38. 170
  39. 168
  40. 108

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