← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 308 · 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 6, 12, 18, …? (a) 468 (b) 72 (c) 504 (d) 936
  2. 2.What is the 34th term of the AP 2, 6, 10, 14, …? (a) 138 (b) 132 (c) 136 (d) 134
  3. 3.Which term of the AP 4, 10, 16, 22, … is 202? (a) 36th (b) 33rd (c) 34th (d) 35th
  4. 4.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 39 (b) 225 (c) 207 (d) 414
  5. 5.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 201 (b) 396 (c) 34 (d) 198
  6. 6.What is the 32nd term of the AP 6, 8, 10, 12, …? (a) 62 (b) 64 (c) 68 (d) 70
  7. 7.Which term of the AP 4, 10, 16, 22, … is 154? (a) 25th (b) 26th (c) 27th (d) 28th
  8. 8.What is the 40th term of the AP 4, 7, 10, 13, …? (a) 120 (b) 121 (c) 124 (d) 117
  9. 9.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 30 (b) 32 (c) 31 (d) 39
  10. 10.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 3906 (c) 1891 (d) 1922
  11. 11.What is the 30th term of the AP 15, 21, 27, 33, …? (a) 189 (b) 174 (c) 180 (d) 195
  12. 12.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 77 (c) 84 (d) 17
  13. 13.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3916 (d) 3828
  14. 14.What is the 16th term of the AP 5, 11, 17, 23, …? (a) 96 (b) 101 (c) 90 (d) 95
  15. 15.What is the 17th term of the AP 7, 14, 21, 28, …? (a) 112 (b) 126 (c) 120 (d) 119
  16. 16.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 312 (b) 156 (c) 168 (d) 24
  17. 17.What is the 25th term of the AP 15, 20, 25, 30, …? (a) 140 (b) 120 (c) 125 (d) 135
  18. 18.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 465 (d) 59
  19. 19.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 5852 (c) 2926 (d) 2850
  20. 20.What is the sum of all the whole numbers from 1 to 46? (a) 2162 (b) 1081 (c) 1035 (d) 1058
  21. 21.What is the 25th term of the AP 14, 20, 26, 32, …? (a) 164 (b) 150 (c) 144 (d) 158
  22. 22.What is the 27th term of the AP 9, 17, 25, 33, …? (a) 216 (b) 208 (c) 217 (d) 225
  23. 23.What is the 40th term of the AP 1, 9, 17, 25, …? (a) 321 (b) 312 (c) 313 (d) 320
  24. 24.What is the 27th term of the AP 9, 11, 13, 15, …? (a) 52 (b) 54 (c) 63 (d) 61
  25. 25.What is the missing term in the AP 10, 16, 22, ?, 34? (a) 29 (b) 34 (c) 27 (d) 28
  26. 26.Which term of the AP 1, 8, 15, 22, … is 99? (a) 15th (b) 17th (c) 16th (d) 14th
  27. 27.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  28. 28.What is the missing term in the AP 9, 17, 25, ?, 41? (a) 34 (b) 32 (c) 33 (d) 41
  29. 29.What is the 31st term of the AP 8, 10, 12, 14, …? (a) 70 (b) 60 (c) 62 (d) 68
  30. 30.What is the 30th term of the AP 2, 7, 12, 17, …? (a) 147 (b) 145 (c) 152 (d) 150
  31. 31.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 27 (b) 20 (c) 21 (d) 22
  32. 32.What is the 25th term of the AP 6, 10, 14, 18, …? (a) 106 (b) 102 (c) 96 (d) 100
  33. 33.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 2346 (c) 2312 (d) 4692
  34. 34.What is the 25th term of the AP 3, 10, 17, 24, …? (a) 168 (b) 175 (c) 178 (d) 171
  35. 35.What is the 28th term of the AP 8, 15, 22, 29, …? (a) 196 (b) 189 (c) 204 (d) 197
  36. 36.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1458 (c) 1485 (d) 2970
  37. 37.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 275 (b) 300 (c) 550 (d) 50
  38. 38.What is the 18th term of the AP 17, 21, 25, 29, …? (a) 68 (b) 72 (c) 85 (d) 89
  39. 39.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 75 (b) 150 (c) 21 (d) 78
  40. 40.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 13 (d) 49

Answer key

  1. 468
  2. 134
  3. 34th
  4. 207
  5. 198
  6. 68
  7. 26th
  8. 121
  9. 31
  10. 1953
  11. 189
  12. 77
  13. 3916
  14. 95
  15. 119
  16. 156
  17. 135
  18. 900
  19. 2926
  20. 1081
  21. 158
  22. 217
  23. 313
  24. 61
  25. 28
  26. 15th
  27. 100
  28. 33
  29. 68
  30. 147
  31. 21
  32. 102
  33. 2346
  34. 171
  35. 197
  36. 1485
  37. 275
  38. 85
  39. 75
  40. 49

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