← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 919 · 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 5 terms of the AP 1, 6, 11, …? (a) 110 (b) 21 (c) 55 (d) 60
  2. 2.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 35 (d) 342
  3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 361 (d) 380
  4. 4.What is the missing term in the AP 20, 23, 26, ?, 32? (a) 28 (b) 30 (c) 32 (d) 29
  5. 5.Which term of the AP 4, 8, 12, 16, … is 136? (a) 34th (b) 33rd (c) 36th (d) 35th
  6. 6.What is the 34th term of the AP 15, 17, 19, 21, …? (a) 68 (b) 83 (c) 66 (d) 81
  7. 7.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 225 (c) 243 (d) 450
  8. 8.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 522 (b) 49 (c) 266 (d) 261
  9. 9.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 462 (c) 231 (d) 232
  10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 231 (d) 441
  11. 11.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 123 (b) 138 (c) 246 (d) 33
  12. 12.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 88 (b) 160 (c) 80 (d) 17
  13. 13.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 230 (b) 115 (c) 16 (d) 120
  14. 14.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4278 (c) 4372 (d) 4371
  15. 15.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 34 (b) 35 (c) 41 (d) 36
  16. 16.Which term of the AP 2, 6, 10, 14, … is 78? (a) 22nd (b) 19th (c) 20th (d) 21st
  17. 17.What is the missing term in the AP 10, ?, 18, 22, 26? (a) 13 (b) 18 (c) 15 (d) 14
  18. 18.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 25 (b) 26 (c) 24 (d) 32
  19. 19.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 49 (b) 46 (c) 42 (d) 45
  20. 20.What is the 17th term of the AP 3, 12, 21, 30, …? (a) 156 (b) 147 (c) 153 (d) 144
  21. 21.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 384 (b) 216 (c) 45 (d) 192
  22. 22.What is the 12th term of the AP 4, 12, 20, 28, …? (a) 96 (b) 100 (c) 92 (d) 88
  23. 23.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 29 (b) 36 (c) 27 (d) 28
  24. 24.What is the 17th term of the AP 4, 10, 16, 22, …? (a) 100 (b) 96 (c) 106 (d) 102
  25. 25.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 22 (b) 21 (c) 26 (d) 23
  26. 26.What is the 27th term of the AP 9, 11, 13, 15, …? (a) 54 (b) 63 (c) 52 (d) 61
  27. 27.Which term of the AP 15, 23, 31, 39, … is 95? (a) 13th (b) 12th (c) 11th (d) 10th
  28. 28.What is the 39th term of the AP 14, 21, 28, 35, …? (a) 280 (b) 273 (c) 266 (d) 287
  29. 29.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 350 (b) 196 (c) 43 (d) 175
  30. 30.What is the 28th term of the AP 2, 8, 14, 20, …? (a) 170 (b) 162 (c) 164 (d) 168
  31. 31.What is the 16th term of the AP 8, 17, 26, 35, …? (a) 152 (b) 135 (c) 143 (d) 144
  32. 32.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 20 (b) 96 (c) 90 (d) 180
  33. 33.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 66 (b) 132 (c) 78 (d) 21
  34. 34.What is the 38th term of the AP 10, 18, 26, 34, …? (a) 304 (b) 314 (c) 306 (d) 296
  35. 35.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 450 (c) 930 (d) 435
  36. 36.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 32 (b) 187 (c) 190 (d) 374
  37. 37.What is the 22nd term of the AP 14, 16, 18, 20, …? (a) 56 (b) 44 (c) 42 (d) 58
  38. 38.What is the 25th term of the AP 14, 17, 20, 23, …? (a) 75 (b) 72 (c) 86 (d) 89
  39. 39.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 196 (d) 210
  40. 40.What is the 32nd term of the AP 2, 5, 8, 11, …? (a) 95 (b) 98 (c) 96 (d) 93

Answer key

  1. 55
  2. 324
  3. 361
  4. 29
  5. 34th
  6. 81
  7. 225
  8. 261
  9. 231
  10. 441
  11. 123
  12. 80
  13. 115
  14. 4371
  15. 35
  16. 20th
  17. 14
  18. 25
  19. 46
  20. 147
  21. 192
  22. 92
  23. 28
  24. 100
  25. 22
  26. 61
  27. 11th
  28. 280
  29. 175
  30. 164
  31. 143
  32. 90
  33. 66
  34. 306
  35. 465
  36. 187
  37. 56
  38. 86
  39. 196
  40. 95

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