← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 275 · 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 6, 14, 22, 30, … is 206? (a) 26th (b) 27th (c) 25th (d) 28th
  2. 2.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 105 (d) 196
  3. 3.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 26 (b) 176 (c) 352 (d) 187
  4. 4.What is the 10th term of the AP 13, 15, 17, 19, …? (a) 20 (b) 33 (c) 31 (d) 18
  5. 5.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 224 (b) 448 (c) 49 (d) 248
  6. 6.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 31 (b) 32 (c) 30 (d) 40
  7. 7.Which term of the AP 12, 15, 18, 21, … is 126? (a) 42nd (b) 40th (c) 39th (d) 38th
  8. 8.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 28 (b) 198 (c) 209 (d) 396
  9. 9.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1250 (c) 1275 (d) 1225
  10. 10.What is the 33rd term of the AP 15, 20, 25, 30, …? (a) 160 (b) 180 (c) 165 (d) 175
  11. 11.What is the 19th term of the AP 12, 14, 16, 18, …? (a) 50 (b) 36 (c) 38 (d) 48
  12. 12.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 39 (b) 162 (c) 144 (d) 288
  13. 13.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  14. 14.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 12 (b) 13 (c) 16 (d) 14
  15. 15.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 31 (b) 33 (c) 38 (d) 32
  16. 16.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 338 (c) 325 (d) 351
  17. 17.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 96 (b) 84 (c) 24 (d) 168
  18. 18.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 207 (b) 39 (c) 225 (d) 414
  19. 19.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 92 (c) 182 (d) 91
  20. 20.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 374 (b) 27 (c) 198 (d) 187
  21. 21.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 930 (c) 450 (d) 435
  22. 22.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 15 (b) 13 (c) 14 (d) 22
  23. 23.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2145 (c) 4422 (d) 2211
  24. 24.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 216 (b) 126 (c) 108 (d) 33
  25. 25.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 23 (b) 70 (c) 130 (d) 65
  26. 26.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4186 (c) 4278 (d) 4232
  27. 27.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 12 (b) 9 (c) 8 (d) 10
  28. 28.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 174 (b) 87 (c) 102 (d) 27
  29. 29.What is the 10th term of the AP 8, 17, 26, 35, …? (a) 81 (b) 89 (c) 90 (d) 98
  30. 30.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 17 (b) 58 (c) 110 (d) 55
  31. 31.What is the 31st term of the AP 1, 4, 7, 10, …? (a) 93 (b) 90 (c) 91 (d) 94
  32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 132 (d) 66
  33. 33.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 154 (b) 80 (c) 20 (d) 77
  34. 34.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 280 (b) 310 (c) 560 (d) 55
  35. 35.What is the 38th term of the AP 14, 23, 32, 41, …? (a) 356 (b) 333 (c) 347 (d) 342
  36. 36.What is the 21st term of the AP 17, 25, 33, 41, …? (a) 168 (b) 177 (c) 160 (d) 185
  37. 37.What is the 22nd term of the AP 3, 7, 11, 15, …? (a) 91 (b) 84 (c) 87 (d) 88
  38. 38.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 636 (b) 336 (c) 318 (d) 43
  39. 39.What is the 10th term of the AP 18, 21, 24, 27, …? (a) 48 (b) 30 (c) 27 (d) 45
  40. 40.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 54 (b) 540 (c) 270 (d) 297

Answer key

  1. 26th
  2. 196
  3. 176
  4. 31
  5. 224
  6. 31
  7. 39th
  8. 198
  9. 1275
  10. 175
  11. 48
  12. 144
  13. 225
  14. 13
  15. 32
  16. 351
  17. 84
  18. 207
  19. 91
  20. 187
  21. 465
  22. 14
  23. 2211
  24. 108
  25. 65
  26. 4278
  27. 9
  28. 87
  29. 89
  30. 55
  31. 91
  32. 121
  33. 77
  34. 280
  35. 347
  36. 177
  37. 87
  38. 318
  39. 45
  40. 270

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