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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 778 · 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 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 78 (c) 77 (d) 154
  2. 2.What is the 13th term of the AP 2, 11, 20, 29, …? (a) 108 (b) 119 (c) 117 (d) 110
  3. 3.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 136 (b) 272 (c) 152 (d) 31
  4. 4.What is the 27th term of the AP 5, 11, 17, 23, …? (a) 167 (b) 156 (c) 162 (d) 161
  5. 5.Which term of the AP 1, 4, 7, 10, … is 91? (a) 33rd (b) 32nd (c) 30th (d) 31st
  6. 6.What is the 15th term of the AP 3, 10, 17, 24, …? (a) 105 (b) 101 (c) 98 (d) 108
  7. 7.What is the 15th term of the AP 13, 20, 27, 34, …? (a) 111 (b) 105 (c) 98 (d) 118
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  9. 9.What is the 27th term of the AP 19, 28, 37, 46, …? (a) 253 (b) 262 (c) 234 (d) 243
  10. 10.Which term of the AP 15, 19, 23, 27, … is 103? (a) 22nd (b) 24th (c) 23rd (d) 25th
  11. 11.What is the 22nd term of the AP 17, 24, 31, 38, …? (a) 154 (b) 171 (c) 164 (d) 147
  12. 12.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 2756 (c) 1378 (d) 1326
  13. 13.What is the 17th term of the AP 17, 25, 33, 41, …? (a) 136 (b) 128 (c) 145 (d) 153
  14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  15. 15.What is the 21st term of the AP 2, 6, 10, 14, …? (a) 82 (b) 86 (c) 80 (d) 84
  16. 16.What is the 22nd term of the AP 1, 3, 5, 7, …? (a) 43 (b) 42 (c) 45 (d) 44
  17. 17.What is the missing term in the AP 2, 9, 16, ?, 30? (a) 23 (b) 22 (c) 24 (d) 30
  18. 18.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 184 (b) 35 (c) 168 (d) 336
  19. 19.What is the 31st term of the AP 9, 12, 15, 18, …? (a) 99 (b) 102 (c) 93 (d) 90
  20. 20.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  21. 21.What is the 21st term of the AP 3, 12, 21, 30, …? (a) 183 (b) 192 (c) 180 (d) 189
  22. 22.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 60 (b) 11 (c) 64 (d) 120
  23. 23.Which term of the AP 16, 21, 26, 31, … is 101? (a) 18th (b) 17th (c) 20th (d) 19th
  24. 24.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 497 (d) 465
  25. 25.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 264 (b) 37 (c) 150 (d) 132
  26. 26.Which term of the AP 7, 12, 17, 22, … is 57? (a) 11th (b) 12th (c) 10th (d) 13th
  27. 27.Which term of the AP 8, 13, 18, 23, … is 98? (a) 20th (b) 21st (c) 19th (d) 18th
  28. 28.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 29 (b) 114 (c) 228 (d) 126
  29. 29.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 882 (c) 903 (d) 861
  30. 30.What is the 38th term of the AP 19, 24, 29, 34, …? (a) 209 (b) 185 (c) 190 (d) 204
  31. 31.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 16 (b) 122 (c) 121 (d) 242
  32. 32.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 121 (c) 240 (d) 120
  33. 33.What is the 24th term of the AP 8, 12, 16, 20, …? (a) 92 (b) 100 (c) 96 (d) 104
  34. 34.What is the 35th term of the AP 10, 12, 14, 16, …? (a) 70 (b) 68 (c) 78 (d) 80
  35. 35.Which term of the AP 16, 18, 20, 22, … is 66? (a) 33rd (b) 27th (c) 25th (d) 26th
  36. 36.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 30 (b) 456 (c) 240 (d) 228
  37. 37.What is the 33rd term of the AP 4, 10, 16, 22, …? (a) 202 (b) 198 (c) 192 (d) 196
  38. 38.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 77 (b) 154 (c) 17 (d) 84
  39. 39.Which term of the AP 11, 16, 21, 26, … is 141? (a) 27th (b) 26th (c) 28th (d) 29th
  40. 40.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 12 (b) 16 (c) 11 (d) 10

Answer key

  1. 77
  2. 110
  3. 136
  4. 161
  5. 31st
  6. 101
  7. 111
  8. 900
  9. 253
  10. 23rd
  11. 164
  12. 1378
  13. 145
  14. 100
  15. 82
  16. 43
  17. 23
  18. 168
  19. 99
  20. 196
  21. 183
  22. 60
  23. 18th
  24. 496
  25. 132
  26. 11th
  27. 19th
  28. 114
  29. 903
  30. 204
  31. 121
  32. 120
  33. 100
  34. 78
  35. 26th
  36. 228
  37. 196
  38. 77
  39. 27th
  40. 11

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