← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 707 · 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.Which term of the AP 6, 10, 14, 18, … is 118? (a) 28th (b) 29th (c) 30th (d) 31st
  2. 2.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1922 (c) 1953 (d) 1891
  3. 3.Which term of the AP 18, 20, 22, 24, … is 58? (a) 21st (b) 20th (c) 29th (d) 22nd
  4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  5. 5.What is the 38th term of the AP 1, 9, 17, 25, …? (a) 305 (b) 304 (c) 296 (d) 297
  6. 6.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 30 (b) 40 (c) 31 (d) 32
  7. 7.What is the 30th term of the AP 5, 8, 11, 14, …? (a) 87 (b) 90 (c) 92 (d) 95
  8. 8.What is the 22nd term of the AP 16, 25, 34, 43, …? (a) 205 (b) 198 (c) 189 (d) 214
  9. 9.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  10. 10.What is the 16th term of the AP 4, 9, 14, 19, …? (a) 75 (b) 79 (c) 80 (d) 84
  11. 11.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 7 (b) 10 (c) 8 (d) 9
  12. 12.What is the 39th term of the AP 8, 12, 16, 20, …? (a) 152 (b) 164 (c) 156 (d) 160
  13. 13.What is the 12th term of the AP 5, 11, 17, 23, …? (a) 71 (b) 66 (c) 77 (d) 72
  14. 14.What is the 40th term of the AP 6, 12, 18, 24, …? (a) 246 (b) 234 (c) 241 (d) 240
  15. 15.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 2926 (c) 3004 (d) 3003
  16. 16.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 35 (b) 280 (c) 140 (d) 145
  17. 17.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 22 (b) 17 (c) 18 (d) 19
  18. 18.What is the 25th term of the AP 11, 20, 29, 38, …? (a) 227 (b) 225 (c) 236 (d) 216
  19. 19.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 228 (b) 29 (c) 432 (d) 216
  20. 20.What is the missing term in the AP 14, ?, 26, 32, 38? (a) 19 (b) 26 (c) 20 (d) 21
  21. 21.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 110 (b) 13 (c) 56 (d) 55
  22. 22.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 17 (b) 130 (c) 70 (d) 65
  23. 23.What is the sum of all the whole numbers from 1 to 66? (a) 2145 (b) 2211 (c) 4422 (d) 2178
  24. 24.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 96 (b) 92 (c) 15 (d) 184
  25. 25.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 132 (b) 37 (c) 150 (d) 264
  26. 26.Which term of the AP 1, 4, 7, 10, … is 43? (a) 16th (b) 14th (c) 17th (d) 15th
  27. 27.What is the 34th term of the AP 17, 20, 23, 26, …? (a) 102 (b) 116 (c) 119 (d) 99
  28. 28.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 231 (c) 232 (d) 462
  29. 29.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 136 (d) 256
  30. 30.What is the 18th term of the AP 12, 21, 30, 39, …? (a) 153 (b) 162 (c) 174 (d) 165
  31. 31.Which term of the AP 4, 10, 16, 22, … is 136? (a) 23rd (b) 24th (c) 22nd (d) 25th
  32. 32.What is the 10th term of the AP 17, 19, 21, 23, …? (a) 20 (b) 18 (c) 37 (d) 35
  33. 33.What is the 13th term of the AP 5, 8, 11, 14, …? (a) 44 (b) 41 (c) 36 (d) 39
  34. 34.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  35. 35.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  36. 36.Which term of the AP 4, 11, 18, 25, … is 74? (a) 12th (b) 13th (c) 10th (d) 11th
  37. 37.What is the 31st term of the AP 14, 21, 28, 35, …? (a) 210 (b) 231 (c) 217 (d) 224
  38. 38.Which term of the AP 3, 8, 13, 18, … is 98? (a) 19th (b) 21st (c) 20th (d) 22nd
  39. 39.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 50 (b) 13 (c) 45 (d) 90
  40. 40.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 32 (c) 120 (d) 204

Answer key

  1. 29th
  2. 1953
  3. 21st
  4. 900
  5. 297
  6. 31
  7. 92
  8. 205
  9. 729
  10. 79
  11. 8
  12. 160
  13. 71
  14. 240
  15. 3003
  16. 140
  17. 18
  18. 227
  19. 216
  20. 20
  21. 55
  22. 65
  23. 2211
  24. 92
  25. 132
  26. 15th
  27. 116
  28. 231
  29. 256
  30. 165
  31. 23rd
  32. 35
  33. 41
  34. 400
  35. 49
  36. 11th
  37. 224
  38. 20th
  39. 45
  40. 102

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