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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 150 · 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 missing term in the AP 20, 22, ?, 26, 28? (a) 25 (b) 26 (c) 24 (d) 23
  2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 55 (d) 19
  3. 3.What is the 29th term of the AP 15, 21, 27, 33, …? (a) 174 (b) 183 (c) 189 (d) 168
  4. 4.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 22 (b) 160 (c) 83 (d) 80
  5. 5.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 145 (b) 290 (c) 19 (d) 150
  6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  8. 8.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 43 (b) 352 (c) 176 (d) 200
  9. 9.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 180 (b) 348 (c) 174 (d) 20
  10. 10.What is the 28th term of the AP 5, 9, 13, 17, …? (a) 108 (b) 113 (c) 112 (d) 117
  11. 11.What is the 38th term of the AP 19, 23, 27, 31, …? (a) 167 (b) 148 (c) 152 (d) 171
  12. 12.Which term of the AP 3, 6, 9, 12, … is 30? (a) 10th (b) 11th (c) 9th (d) 12th
  13. 13.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 160 (b) 90 (c) 80 (d) 24
  14. 14.What is the missing term in the AP 9, 17, 25, ?, 41? (a) 41 (b) 33 (c) 34 (d) 32
  15. 15.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2888 (c) 2850 (d) 2926
  16. 16.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 216 (b) 109 (c) 16 (d) 108
  17. 17.What is the 27th term of the AP 16, 19, 22, 25, …? (a) 94 (b) 97 (c) 78 (d) 81
  18. 18.What is the 36th term of the AP 12, 19, 26, 33, …? (a) 252 (b) 257 (c) 245 (d) 264
  19. 19.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 300 (c) 650 (d) 326
  20. 20.What is the 25th term of the AP 1, 6, 11, 16, …? (a) 120 (b) 125 (c) 121 (d) 126
  21. 21.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 21 (b) 26 (c) 22 (d) 20
  22. 22.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 144 (b) 288 (c) 162 (d) 39
  23. 23.Which term of the AP 1, 10, 19, 28, … is 100? (a) 13th (b) 12th (c) 11th (d) 14th
  24. 24.What is the 33rd term of the AP 13, 16, 19, 22, …? (a) 99 (b) 109 (c) 96 (d) 112
  25. 25.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 23 (b) 85 (c) 75 (d) 150
  26. 26.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 2016 (c) 4032 (d) 1953
  27. 27.Which term of the AP 13, 21, 29, 37, … is 229? (a) 27th (b) 29th (c) 30th (d) 28th
  28. 28.What is the 20th term of the AP 5, 13, 21, 29, …? (a) 160 (b) 157 (c) 165 (d) 152
  29. 29.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 252 (b) 127 (c) 18 (d) 126
  30. 30.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2211 (c) 2145 (d) 4422
  31. 31.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 19 (b) 18 (c) 17 (d) 16
  32. 32.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 90 (b) 48 (c) 10 (d) 45
  33. 33.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 968 (c) 990 (d) 1980
  34. 34.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 36 (d) 21
  35. 35.What is the missing term in the AP 16, 20, 24, ?, 32? (a) 32 (b) 28 (c) 27 (d) 29
  36. 36.Which term of the AP 4, 7, 10, 13, … is 37? (a) 11th (b) 13th (c) 14th (d) 12th
  37. 37.What is the 11th term of the AP 14, 17, 20, 23, …? (a) 47 (b) 30 (c) 44 (d) 33
  38. 38.What is the 36th term of the AP 2, 5, 8, 11, …? (a) 110 (b) 107 (c) 108 (d) 105
  39. 39.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  40. 40.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 42 (b) 234 (c) 468 (d) 252

Answer key

  1. 24
  2. 100
  3. 183
  4. 80
  5. 145
  6. 529
  7. 324
  8. 176
  9. 174
  10. 113
  11. 167
  12. 10th
  13. 80
  14. 33
  15. 2926
  16. 108
  17. 94
  18. 257
  19. 325
  20. 121
  21. 21
  22. 144
  23. 12th
  24. 109
  25. 75
  26. 2016
  27. 28th
  28. 157
  29. 126
  30. 2211
  31. 17
  32. 45
  33. 990
  34. 36
  35. 28
  36. 12th
  37. 44
  38. 107
  39. 25
  40. 234

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