← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 433 · 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 13, 15, 17, 19, … is 47? (a) 17th (b) 18th (c) 19th (d) 20th
  2. 2.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 252 (b) 49 (c) 450 (d) 225
  3. 3.What is the 20th term of the AP 8, 17, 26, 35, …? (a) 179 (b) 171 (c) 180 (d) 188
  4. 4.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 861 (c) 882 (d) 903
  5. 5.What is the 26th term of the AP 6, 15, 24, 33, …? (a) 240 (b) 231 (c) 225 (d) 234
  6. 6.What is the 38th term of the AP 3, 9, 15, 21, …? (a) 225 (b) 228 (c) 222 (d) 231
  7. 7.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 105 (b) 210 (c) 25 (d) 114
  8. 8.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2888 (c) 2850 (d) 2926
  9. 9.What is the 10th term of the AP 10, 15, 20, 25, …? (a) 55 (b) 50 (c) 45 (d) 60
  10. 10.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 112 (b) 56 (c) 14 (d) 63
  11. 11.What is the 26th term of the AP 7, 14, 21, 28, …? (a) 183 (b) 189 (c) 175 (d) 182
  12. 12.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 294 (b) 168 (c) 147 (d) 39
  13. 13.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 2352 (c) 1176 (d) 1128
  14. 14.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 70 (c) 8 (d) 35
  15. 15.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 8 (b) 10 (c) 15 (d) 9
  16. 16.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 21 (b) 20 (c) 18 (d) 19
  17. 17.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  18. 18.What is the 36th term of the AP 7, 12, 17, 22, …? (a) 175 (b) 180 (c) 182 (d) 187
  19. 19.What is the 27th term of the AP 15, 17, 19, 21, …? (a) 52 (b) 67 (c) 69 (d) 54
  20. 20.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 350 (b) 175 (c) 43 (d) 196
  21. 21.What is the 27th term of the AP 6, 14, 22, 30, …? (a) 208 (b) 214 (c) 222 (d) 216
  22. 22.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 45 (c) 110 (d) 55
  23. 23.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 182 (d) 91
  24. 24.What is the 25th term of the AP 10, 18, 26, 34, …? (a) 210 (b) 200 (c) 192 (d) 202
  25. 25.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 19 (b) 18 (c) 26 (d) 20
  26. 26.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 190 (c) 171 (d) 380
  27. 27.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 126 (b) 222 (c) 31 (d) 111
  28. 28.What is the 19th term of the AP 14, 20, 26, 32, …? (a) 128 (b) 114 (c) 108 (d) 122
  29. 29.Which term of the AP 12, 20, 28, 36, … is 140? (a) 16th (b) 19th (c) 17th (d) 18th
  30. 30.Which term of the AP 16, 20, 24, 28, … is 136? (a) 34th (b) 31st (c) 30th (d) 32nd
  31. 31.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 85 (b) 27 (c) 90 (d) 170
  32. 32.What is the 20th term of the AP 4, 13, 22, 31, …? (a) 180 (b) 184 (c) 175 (d) 171
  33. 33.Which term of the AP 10, 12, 14, 16, … is 34? (a) 13th (b) 17th (c) 14th (d) 12th
  34. 34.What is the 25th term of the AP 2, 4, 6, 8, …? (a) 51 (b) 52 (c) 48 (d) 50
  35. 35.What is the 20th term of the AP 5, 14, 23, 32, …? (a) 185 (b) 180 (c) 171 (d) 176
  36. 36.What is the missing term in the AP 12, 18, ?, 30, 36? (a) 25 (b) 23 (c) 30 (d) 24
  37. 37.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 180 (b) 36 (c) 198 (d) 360
  38. 38.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 4005 (c) 3916 (d) 4006
  39. 39.Which term of the AP 19, 26, 33, 40, … is 110? (a) 16th (b) 14th (c) 15th (d) 13th
  40. 40.What is the 38th term of the AP 16, 19, 22, 25, …? (a) 127 (b) 130 (c) 111 (d) 114

Answer key

  1. 18th
  2. 225
  3. 179
  4. 903
  5. 231
  6. 225
  7. 105
  8. 2926
  9. 55
  10. 56
  11. 182
  12. 147
  13. 1176
  14. 35
  15. 9
  16. 19
  17. 729
  18. 182
  19. 67
  20. 175
  21. 214
  22. 55
  23. 169
  24. 202
  25. 19
  26. 190
  27. 111
  28. 122
  29. 17th
  30. 31st
  31. 85
  32. 175
  33. 13th
  34. 50
  35. 176
  36. 24
  37. 180
  38. 4005
  39. 14th
  40. 127

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