← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 244 · 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 2, 6, 10, 14, … is 42? (a) 12th (b) 10th (c) 13th (d) 11th
  2. 2.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 336 (b) 624 (c) 312 (d) 48
  3. 3.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 182 (c) 91 (d) 78
  4. 4.What is the 31st term of the AP 14, 21, 28, 35, …? (a) 224 (b) 231 (c) 217 (d) 210
  5. 5.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 21 (b) 20 (c) 23 (d) 19
  6. 6.What is the 11th term of the AP 2, 10, 18, 26, …? (a) 82 (b) 90 (c) 88 (d) 80
  7. 7.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  8. 8.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1711 (c) 3540 (d) 1770
  9. 9.Which term of the AP 18, 20, 22, 24, … is 84? (a) 35th (b) 34th (c) 42nd (d) 33rd
  10. 10.What is the 11th term of the AP 4, 6, 8, 10, …? (a) 26 (b) 20 (c) 22 (d) 24
  11. 11.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 44 (b) 34 (c) 35 (d) 36
  12. 12.What is the 37th term of the AP 10, 19, 28, 37, …? (a) 333 (b) 324 (c) 343 (d) 334
  13. 13.What is the 17th term of the AP 17, 23, 29, 35, …? (a) 102 (b) 119 (c) 113 (d) 96
  14. 14.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 17 (b) 26 (c) 18 (d) 19
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  16. 16.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 722 (c) 1482 (d) 703
  17. 17.Which term of the AP 14, 19, 24, 29, … is 59? (a) 11th (b) 10th (c) 9th (d) 12th
  18. 18.Which term of the AP 20, 25, 30, 35, … is 210? (a) 38th (b) 42nd (c) 40th (d) 39th
  19. 19.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 210 (b) 380 (c) 190 (d) 37
  20. 20.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 13 (b) 140 (c) 70 (d) 71
  21. 21.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 14 (b) 15 (c) 22 (d) 16
  22. 22.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 43 (b) 14 (c) 40 (d) 80
  23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
  24. 24.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 150 (b) 84 (c) 20 (d) 75
  25. 25.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 60 (c) 114 (d) 12
  26. 26.Which term of the AP 5, 14, 23, 32, … is 221? (a) 27th (b) 26th (c) 25th (d) 24th
  27. 27.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 25 (b) 75 (c) 150 (d) 80
  28. 28.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 3916 (c) 4005 (d) 4006
  29. 29.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 27 (b) 28 (c) 29 (d) 37
  30. 30.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 990 (c) 968 (d) 946
  31. 31.What is the 14th term of the AP 20, 24, 28, 32, …? (a) 56 (b) 52 (c) 76 (d) 72
  32. 32.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 171 (b) 342 (c) 31 (d) 174
  33. 33.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 18 (b) 20 (c) 25 (d) 19
  34. 34.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 406 (d) 55
  35. 35.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 15 (b) 18 (c) 17 (d) 16
  36. 36.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 23 (b) 20 (c) 18 (d) 19
  37. 37.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5050 (c) 5000 (d) 4950
  38. 38.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 24 (b) 308 (c) 154 (d) 165
  39. 39.What is the 38th term of the AP 13, 17, 21, 25, …? (a) 148 (b) 165 (c) 152 (d) 161
  40. 40.What is the 33rd term of the AP 13, 16, 19, 22, …? (a) 112 (b) 96 (c) 109 (d) 99

Answer key

  1. 11th
  2. 312
  3. 91
  4. 224
  5. 20
  6. 82
  7. 121
  8. 1770
  9. 34th
  10. 24
  11. 35
  12. 334
  13. 113
  14. 18
  15. 100
  16. 741
  17. 10th
  18. 39th
  19. 190
  20. 70
  21. 15
  22. 40
  23. 225
  24. 75
  25. 57
  26. 25th
  27. 75
  28. 4005
  29. 28
  30. 990
  31. 72
  32. 171
  33. 19
  34. 784
  35. 16
  36. 19
  37. 5050
  38. 154
  39. 161
  40. 109

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