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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 199 · 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 3, 7, ?, 15, 19? (a) 10 (b) 12 (c) 15 (d) 11
  2. 2.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 60 (c) 30 (d) 10
  3. 3.What is the 12th term of the AP 12, 18, 24, 30, …? (a) 84 (b) 66 (c) 72 (d) 78
  4. 4.Which term of the AP 18, 20, 22, 24, … is 38? (a) 11th (b) 12th (c) 10th (d) 19th
  5. 5.Which term of the AP 7, 13, 19, 25, … is 235? (a) 41st (b) 39th (c) 40th (d) 38th
  6. 6.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 325 (d) 300
  7. 7.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 77 (c) 78 (d) 12
  8. 8.What is the 36th term of the AP 3, 5, 7, 9, …? (a) 75 (b) 70 (c) 72 (d) 73
  9. 9.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 90 (b) 13 (c) 96 (d) 180
  10. 10.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 320 (b) 170 (c) 25 (d) 160
  11. 11.What is the 21st term of the AP 20, 27, 34, 41, …? (a) 160 (b) 140 (c) 147 (d) 167
  12. 12.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 6 (b) 21 (c) 40 (d) 20
  13. 13.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  14. 14.What is the sum of all the whole numbers from 1 to 82? (a) 3321 (b) 3362 (c) 3403 (d) 6806
  15. 15.What is the 21st term of the AP 10, 17, 24, 31, …? (a) 150 (b) 147 (c) 140 (d) 157
  16. 16.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 26 (b) 192 (c) 108 (d) 96
  17. 17.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 595 (c) 578 (d) 1190
  18. 18.What is the 33rd term of the AP 3, 8, 13, 18, …? (a) 168 (b) 165 (c) 163 (d) 160
  19. 19.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 144 (b) 147 (c) 28 (d) 288
  20. 20.What is the 23rd term of the AP 9, 14, 19, 24, …? (a) 124 (b) 115 (c) 110 (d) 119
  21. 21.What is the 40th term of the AP 20, 22, 24, 26, …? (a) 100 (b) 78 (c) 80 (d) 98
  22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 210 (d) 39
  23. 23.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 37 (c) 132 (d) 264
  24. 24.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
  25. 25.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 18 (b) 17 (c) 16 (d) 20
  26. 26.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1891 (c) 1953 (d) 1922
  27. 27.Which term of the AP 8, 11, 14, 17, … is 32? (a) 8th (b) 9th (c) 10th (d) 11th
  28. 28.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 25 (b) 168 (c) 180 (d) 336
  29. 29.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 91 (c) 182 (d) 25
  30. 30.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 222 (b) 31 (c) 126 (d) 111
  31. 31.What is the 14th term of the AP 20, 25, 30, 35, …? (a) 65 (b) 70 (c) 90 (d) 85
  32. 32.What is the 29th term of the AP 4, 6, 8, 10, …? (a) 56 (b) 60 (c) 62 (d) 58
  33. 33.What is the 16th term of the AP 20, 26, 32, 38, …? (a) 96 (b) 90 (c) 110 (d) 116
  34. 34.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 650 (d) 49
  35. 35.What is the sum of all the whole numbers from 1 to 55? (a) 3080 (b) 1541 (c) 1485 (d) 1540
  36. 36.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 900 (c) 59 (d) 930
  37. 37.What is the 33rd term of the AP 2, 11, 20, 29, …? (a) 288 (b) 297 (c) 299 (d) 290
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  39. 39.What is the 23rd term of the AP 18, 26, 34, 42, …? (a) 184 (b) 194 (c) 176 (d) 202
  40. 40.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 171 (b) 324 (c) 162 (d) 26

Answer key

  1. 11
  2. 30
  3. 78
  4. 11th
  5. 39th
  6. 325
  7. 77
  8. 73
  9. 90
  10. 160
  11. 160
  12. 20
  13. 100
  14. 3403
  15. 150
  16. 96
  17. 595
  18. 163
  19. 144
  20. 119
  21. 98
  22. 400
  23. 132
  24. 324
  25. 17
  26. 1953
  27. 9th
  28. 168
  29. 169
  30. 111
  31. 85
  32. 60
  33. 110
  34. 625
  35. 1540
  36. 900
  37. 290
  38. 25
  39. 194
  40. 162

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