← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 556 · 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 all the whole numbers from 1 to 23? (a) 253 (b) 276 (c) 277 (d) 552
  2. 2.What is the missing term in the AP 19, 25, 31, ?, 43? (a) 37 (b) 43 (c) 36 (d) 38
  3. 3.What is the 11th term of the AP 15, 19, 23, 27, …? (a) 40 (b) 44 (c) 59 (d) 55
  4. 4.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 17 (b) 55 (c) 110 (d) 58
  5. 5.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 2628 (c) 5402 (d) 2701
  6. 6.What is the 13th term of the AP 14, 17, 20, 23, …? (a) 50 (b) 53 (c) 39 (d) 36
  7. 7.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 180 (b) 99 (c) 90 (d) 18
  8. 8.Which term of the AP 10, 19, 28, 37, … is 136? (a) 16th (b) 15th (c) 17th (d) 14th
  9. 9.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 243 (b) 51 (c) 270 (d) 486
  10. 10.What is the 25th term of the AP 17, 20, 23, 26, …? (a) 72 (b) 75 (c) 89 (d) 92
  11. 11.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 22 (b) 20 (c) 21 (d) 25
  12. 12.What is the 11th term of the AP 6, 15, 24, 33, …? (a) 99 (b) 96 (c) 105 (d) 90
  13. 13.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 12 (b) 64 (c) 126 (d) 63
  14. 14.What is the missing term in the AP 15, ?, 19, 21, 23? (a) 16 (b) 19 (c) 17 (d) 18
  15. 15.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 80 (b) 13 (c) 152 (d) 76
  16. 16.What is the 36th term of the AP 13, 20, 27, 34, …? (a) 252 (b) 265 (c) 258 (d) 245
  17. 17.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 162 (b) 34 (c) 180 (d) 324
  18. 18.What is the 23rd term of the AP 9, 11, 13, 15, …? (a) 53 (b) 44 (c) 46 (d) 55
  19. 19.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 6 (b) 8 (c) 9 (d) 7
  20. 20.What is the 32nd term of the AP 3, 8, 13, 18, …? (a) 158 (b) 160 (c) 163 (d) 155
  21. 21.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 12 (b) 77 (c) 154 (d) 78
  22. 22.Which term of the AP 19, 22, 25, 28, … is 52? (a) 14th (b) 13th (c) 11th (d) 12th
  23. 23.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 947 (c) 903 (d) 946
  24. 24.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 231 (b) 440 (c) 220 (d) 30
  25. 25.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 368 (b) 37 (c) 200 (d) 184
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
  27. 27.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 210 (d) 196
  28. 28.What is the 31st term of the AP 5, 11, 17, 23, …? (a) 191 (b) 186 (c) 185 (d) 180
  29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 47 (d) 300
  30. 30.What is the 18th term of the AP 3, 5, 7, 9, …? (a) 39 (b) 36 (c) 34 (d) 37
  31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 49 (d) 56
  32. 32.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 110 (c) 120 (d) 20
  33. 33.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
  34. 34.What is the 29th term of the AP 3, 10, 17, 24, …? (a) 206 (b) 199 (c) 196 (d) 203
  35. 35.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 11 (b) 45 (c) 46 (d) 90
  36. 36.What is the 13th term of the AP 17, 23, 29, 35, …? (a) 78 (b) 72 (c) 95 (d) 89
  37. 37.What is the 34th term of the AP 5, 8, 11, 14, …? (a) 99 (b) 102 (c) 107 (d) 104
  38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 41 (d) 231
  39. 39.What is the 18th term of the AP 7, 12, 17, 22, …? (a) 92 (b) 90 (c) 97 (d) 85
  40. 40.What is the 23rd term of the AP 20, 27, 34, 41, …? (a) 161 (b) 174 (c) 154 (d) 181

Answer key

  1. 276
  2. 37
  3. 55
  4. 55
  5. 2701
  6. 50
  7. 90
  8. 15th
  9. 243
  10. 89
  11. 21
  12. 96
  13. 63
  14. 17
  15. 76
  16. 258
  17. 162
  18. 53
  19. 7
  20. 158
  21. 77
  22. 12th
  23. 946
  24. 220
  25. 184
  26. 841
  27. 196
  28. 185
  29. 576
  30. 37
  31. 49
  32. 110
  33. 81
  34. 199
  35. 45
  36. 89
  37. 104
  38. 441
  39. 92
  40. 174

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