← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 952 · 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 12 terms of the AP 10, 16, 22, …? (a) 516 (b) 552 (c) 1032 (d) 76
  2. 2.What is the 12th term of the AP 6, 9, 12, 15, …? (a) 39 (b) 42 (c) 36 (d) 33
  3. 3.What is the missing term in the AP 6, 12, ?, 24, 30? (a) 17 (b) 18 (c) 19 (d) 24
  4. 4.Which term of the AP 2, 4, 6, 8, … is 22? (a) 10th (b) 13th (c) 11th (d) 12th
  5. 5.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 27 (b) 252 (c) 129 (d) 126
  6. 6.What is the 38th term of the AP 9, 14, 19, 24, …? (a) 185 (b) 194 (c) 199 (d) 190
  7. 7.What is the 17th term of the AP 16, 25, 34, 43, …? (a) 153 (b) 169 (c) 144 (d) 160
  8. 8.What is the 14th term of the AP 1, 4, 7, 10, …? (a) 42 (b) 39 (c) 43 (d) 40
  9. 9.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 16 (b) 72 (c) 66 (d) 132
  10. 10.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 126 (b) 127 (c) 252 (d) 18
  11. 11.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 27 (b) 102 (c) 174 (d) 87
  12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 380 (d) 37
  13. 13.What is the 34th term of the AP 15, 23, 31, 39, …? (a) 264 (b) 287 (c) 279 (d) 272
  14. 14.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 38 (b) 32 (c) 30 (d) 31
  15. 15.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 61 (b) 14 (c) 60 (d) 120
  16. 16.What is the 16th term of the AP 15, 23, 31, 39, …? (a) 143 (b) 128 (c) 135 (d) 120
  17. 17.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4095 (c) 4187 (d) 4186
  18. 18.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 91 (b) 105 (c) 182 (d) 25
  19. 19.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 28 (d) 56
  20. 20.Which term of the AP 2, 10, 18, 26, … is 66? (a) 11th (b) 10th (c) 9th (d) 8th
  21. 21.What is the 37th term of the AP 17, 19, 21, 23, …? (a) 91 (b) 89 (c) 74 (d) 72
  22. 22.Which term of the AP 1, 9, 17, 25, … is 249? (a) 33rd (b) 32nd (c) 31st (d) 34th
  23. 23.What is the 24th term of the AP 16, 19, 22, 25, …? (a) 69 (b) 85 (c) 88 (d) 72
  24. 24.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 16 (b) 126 (c) 132 (d) 252
  25. 25.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 64 (b) 370 (c) 400 (d) 740
  26. 26.Which term of the AP 17, 19, 21, 23, … is 43? (a) 16th (b) 14th (c) 13th (d) 15th
  27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 15 (d) 64
  28. 28.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 33 (b) 23 (c) 25 (d) 24
  29. 29.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 42 (b) 203 (c) 198 (d) 396
  30. 30.What is the 31st term of the AP 12, 15, 18, 21, …? (a) 90 (b) 105 (c) 102 (d) 93
  31. 31.Which term of the AP 10, 16, 22, 28, … is 82? (a) 13th (b) 15th (c) 12th (d) 14th
  32. 32.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 200 (b) 32 (c) 370 (d) 185
  33. 33.Which term of the AP 6, 12, 18, 24, … is 54? (a) 11th (b) 10th (c) 9th (d) 8th
  34. 34.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 85 (b) 29 (c) 170 (d) 100
  35. 35.Which term of the AP 5, 11, 17, 23, … is 119? (a) 19th (b) 20th (c) 22nd (d) 21st
  36. 36.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 5550 (c) 2701 (d) 2738
  37. 37.What is the 23rd term of the AP 6, 13, 20, 27, …? (a) 154 (b) 161 (c) 160 (d) 167
  38. 38.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 49 (b) 50 (c) 10 (d) 98
  39. 39.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 330 (b) 166 (c) 20 (d) 165
  40. 40.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 35 (b) 140 (c) 280 (d) 145

Answer key

  1. 516
  2. 39
  3. 18
  4. 11th
  5. 126
  6. 194
  7. 160
  8. 40
  9. 66
  10. 126
  11. 87
  12. 361
  13. 279
  14. 31
  15. 60
  16. 135
  17. 4186
  18. 91
  19. 49
  20. 9th
  21. 89
  22. 32nd
  23. 85
  24. 126
  25. 370
  26. 14th
  27. 64
  28. 24
  29. 198
  30. 102
  31. 13th
  32. 185
  33. 9th
  34. 85
  35. 20th
  36. 2775
  37. 160
  38. 49
  39. 165
  40. 140

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad