← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 784 · 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 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 300 (d) 600
  2. 2.Which term of the AP 5, 14, 23, 32, … is 338? (a) 38th (b) 40th (c) 37th (d) 39th
  3. 3.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 38 (b) 32 (c) 31 (d) 30
  4. 4.What is the 15th term of the AP 3, 10, 17, 24, …? (a) 101 (b) 105 (c) 108 (d) 98
  5. 5.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 12 (b) 10 (c) 11 (d) 18
  6. 6.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 56 (d) 28
  7. 7.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1431 (c) 1458 (d) 1485
  8. 8.What is the 23rd term of the AP 11, 13, 15, 17, …? (a) 57 (b) 55 (c) 44 (d) 46
  9. 9.What is the 25th term of the AP 12, 20, 28, 36, …? (a) 204 (b) 192 (c) 200 (d) 212
  10. 10.What is the 11th term of the AP 9, 18, 27, 36, …? (a) 99 (b) 90 (c) 100 (d) 108
  11. 11.What is the missing term in the AP 13, 18, 23, ?, 33? (a) 29 (b) 27 (c) 33 (d) 28
  12. 12.What is the sum of all the whole numbers from 1 to 90? (a) 8190 (b) 4095 (c) 4005 (d) 4050
  13. 13.What is the 39th term of the AP 16, 22, 28, 34, …? (a) 244 (b) 228 (c) 234 (d) 250
  14. 14.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 25 (c) 170 (d) 320
  15. 15.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 132 (d) 21
  16. 16.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1653 (c) 3306 (d) 1654
  17. 17.Which term of the AP 17, 21, 25, 29, … is 93? (a) 19th (b) 20th (c) 21st (d) 22nd
  18. 18.Which term of the AP 7, 11, 15, 19, … is 95? (a) 24th (b) 25th (c) 22nd (d) 23rd
  19. 19.Which term of the AP 18, 23, 28, 33, … is 73? (a) 11th (b) 12th (c) 13th (d) 14th
  20. 20.What is the 33rd term of the AP 14, 20, 26, 32, …? (a) 192 (b) 212 (c) 198 (d) 206
  21. 21.What is the 37th term of the AP 15, 22, 29, 36, …? (a) 267 (b) 274 (c) 252 (d) 259
  22. 22.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2485 (c) 2557 (d) 2556
  23. 23.What is the 19th term of the AP 19, 21, 23, 25, …? (a) 55 (b) 38 (c) 57 (d) 36
  24. 24.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 550 (b) 45 (c) 275 (d) 297
  25. 25.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 490 (b) 245 (c) 47 (d) 270
  26. 26.Which term of the AP 10, 14, 18, 22, … is 54? (a) 14th (b) 12th (c) 11th (d) 13th
  27. 27.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 448 (b) 248 (c) 49 (d) 224
  28. 28.What is the 30th term of the AP 16, 19, 22, 25, …? (a) 106 (b) 87 (c) 90 (d) 103
  29. 29.What is the 13th term of the AP 9, 11, 13, 15, …? (a) 26 (b) 24 (c) 33 (d) 35
  30. 30.What is the 29th term of the AP 13, 15, 17, 19, …? (a) 71 (b) 58 (c) 56 (d) 69
  31. 31.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 37 (b) 308 (c) 159 (d) 154
  32. 32.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 29 (b) 22 (c) 23 (d) 24
  33. 33.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 444 (b) 222 (c) 35 (d) 240
  34. 34.What is the 24th term of the AP 13, 21, 29, 37, …? (a) 184 (b) 205 (c) 192 (d) 197
  35. 35.What is the 11th term of the AP 13, 22, 31, 40, …? (a) 103 (b) 99 (c) 90 (d) 112
  36. 36.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 135 (c) 22 (d) 126
  37. 37.What is the 17th term of the AP 3, 11, 19, 27, …? (a) 139 (b) 136 (c) 128 (d) 131
  38. 38.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 400 (b) 220 (c) 38 (d) 200
  39. 39.What is the 34th term of the AP 19, 21, 23, 25, …? (a) 66 (b) 68 (c) 85 (d) 87
  40. 40.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 144 (b) 258 (c) 129 (d) 34

Answer key

  1. 576
  2. 38th
  3. 31
  4. 101
  5. 11
  6. 49
  7. 1485
  8. 55
  9. 204
  10. 99
  11. 28
  12. 4095
  13. 244
  14. 160
  15. 121
  16. 1653
  17. 20th
  18. 23rd
  19. 12th
  20. 206
  21. 267
  22. 2556
  23. 55
  24. 275
  25. 245
  26. 12th
  27. 224
  28. 103
  29. 33
  30. 69
  31. 154
  32. 23
  33. 222
  34. 197
  35. 103
  36. 126
  37. 131
  38. 200
  39. 85
  40. 129

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