← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 525 · 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 21st term of the AP 6, 10, 14, 18, …? (a) 86 (b) 84 (c) 80 (d) 90
  2. 2.What is the sum of all the whole numbers from 1 to 55? (a) 3080 (b) 1540 (c) 1541 (d) 1485
  3. 3.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  4. 4.What is the missing term in the AP 20, 24, 28, ?, 36? (a) 32 (b) 36 (c) 33 (d) 31
  5. 5.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 126 (b) 63 (c) 72 (d) 18
  6. 6.What is the 15th term of the AP 7, 11, 15, 19, …? (a) 67 (b) 56 (c) 60 (d) 63
  7. 7.Which term of the AP 18, 27, 36, 45, … is 189? (a) 22nd (b) 19th (c) 21st (d) 20th
  8. 8.Which term of the AP 12, 14, 16, 18, … is 36? (a) 18th (b) 12th (c) 13th (d) 14th
  9. 9.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 702 (c) 338 (d) 351
  10. 10.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 13 (b) 15 (c) 18 (d) 14
  11. 11.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4418 (c) 4371 (d) 8930
  12. 12.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 326 (c) 650 (d) 325
  13. 13.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 108 (c) 54 (d) 10
  14. 14.What is the 21st term of the AP 5, 7, 9, 11, …? (a) 45 (b) 40 (c) 47 (d) 42
  15. 15.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 23 (b) 21 (c) 22 (d) 30
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
  17. 17.What is the 21st term of the AP 17, 19, 21, 23, …? (a) 59 (b) 40 (c) 57 (d) 42
  18. 18.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 130 (b) 21 (c) 240 (d) 120
  19. 19.Which term of the AP 17, 25, 33, 41, … is 177? (a) 23rd (b) 20th (c) 22nd (d) 21st
  20. 20.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 276 (c) 600 (d) 288
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 132 (d) 21
  22. 22.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 17 (b) 72 (c) 144 (d) 78
  23. 23.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 112 (b) 21 (c) 120 (d) 224
  24. 24.Which term of the AP 17, 23, 29, 35, … is 131? (a) 21st (b) 19th (c) 22nd (d) 20th
  25. 25.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 903 (c) 882 (d) 1806
  26. 26.What is the 36th term of the AP 6, 11, 16, 21, …? (a) 175 (b) 181 (c) 180 (d) 186
  27. 27.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2080 (c) 2146 (d) 2145
  28. 28.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 10 (b) 9 (c) 12 (d) 8
  29. 29.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 34 (b) 28 (c) 27 (d) 26
  30. 30.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 19 (b) 308 (c) 154 (d) 155
  31. 31.What is the 30th term of the AP 11, 13, 15, 17, …? (a) 71 (b) 58 (c) 60 (d) 69
  32. 32.What is the 32nd term of the AP 5, 14, 23, 32, …? (a) 279 (b) 284 (c) 288 (d) 293
  33. 33.Which term of the AP 15, 18, 21, 24, … is 132? (a) 40th (b) 39th (c) 44th (d) 41st
  34. 34.What is the 18th term of the AP 10, 15, 20, 25, …? (a) 90 (b) 95 (c) 100 (d) 85
  35. 35.What is the 25th term of the AP 7, 14, 21, 28, …? (a) 182 (b) 175 (c) 168 (d) 176
  36. 36.Which term of the AP 9, 11, 13, 15, … is 45? (a) 21st (b) 20th (c) 19th (d) 18th
  37. 37.What is the 36th term of the AP 12, 14, 16, 18, …? (a) 84 (b) 82 (c) 72 (d) 70
  38. 38.What is the 28th term of the AP 20, 24, 28, 32, …? (a) 128 (b) 112 (c) 132 (d) 108
  39. 39.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 280 (b) 140 (c) 161 (d) 38
  40. 40.What is the 13th term of the AP 5, 7, 9, 11, …? (a) 26 (b) 24 (c) 29 (d) 31

Answer key

  1. 86
  2. 1540
  3. 91
  4. 32
  5. 63
  6. 63
  7. 20th
  8. 13th
  9. 351
  10. 14
  11. 4465
  12. 325
  13. 54
  14. 45
  15. 22
  16. 81
  17. 57
  18. 120
  19. 21st
  20. 300
  21. 121
  22. 72
  23. 112
  24. 20th
  25. 903
  26. 181
  27. 2145
  28. 9
  29. 27
  30. 154
  31. 69
  32. 284
  33. 40th
  34. 95
  35. 175
  36. 19th
  37. 82
  38. 128
  39. 140
  40. 29

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