← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 610 · 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 89? (a) 4006 (b) 8010 (c) 4005 (d) 3916
  2. 2.What is the missing term in the AP 20, ?, 32, 38, 44? (a) 26 (b) 32 (c) 27 (d) 25
  3. 3.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 22 (b) 16 (c) 14 (d) 15
  4. 4.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 8556 (c) 4186 (d) 4278
  5. 5.What is the 32nd term of the AP 14, 20, 26, 32, …? (a) 186 (b) 206 (c) 192 (d) 200
  6. 6.What is the 39th term of the AP 1, 7, 13, 19, …? (a) 235 (b) 228 (c) 234 (d) 229
  7. 7.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4802 (c) 4851 (d) 4753
  8. 8.What is the 21st term of the AP 1, 10, 19, 28, …? (a) 180 (b) 190 (c) 181 (d) 189
  9. 9.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 100 (b) 104 (c) 16 (d) 200
  10. 10.What is the 37th term of the AP 5, 12, 19, 26, …? (a) 252 (b) 259 (c) 264 (d) 257
  11. 11.What is the 36th term of the AP 14, 18, 22, 26, …? (a) 154 (b) 144 (c) 140 (d) 158
  12. 12.What is the 25th term of the AP 14, 20, 26, 32, …? (a) 150 (b) 144 (c) 158 (d) 164
  13. 13.What is the 34th term of the AP 17, 26, 35, 44, …? (a) 323 (b) 314 (c) 297 (d) 306
  14. 14.What is the 37th term of the AP 13, 21, 29, 37, …? (a) 288 (b) 309 (c) 301 (d) 296
  15. 15.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 231 (d) 210
  16. 16.What is the 37th term of the AP 6, 10, 14, 18, …? (a) 148 (b) 150 (c) 154 (d) 144
  17. 17.Which term of the AP 16, 19, 22, 25, … is 127? (a) 40th (b) 37th (c) 39th (d) 38th
  18. 18.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 342 (c) 171 (d) 162
  19. 19.What is the 22nd term of the AP 6, 8, 10, 12, …? (a) 48 (b) 42 (c) 50 (d) 44
  20. 20.What is the 14th term of the AP 15, 17, 19, 21, …? (a) 28 (b) 41 (c) 43 (d) 26
  21. 21.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 80 (b) 140 (c) 70 (d) 22
  22. 22.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 49 (b) 522 (c) 261 (d) 266
  23. 23.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 338 (c) 702 (d) 325
  24. 24.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 408 (b) 54 (c) 768 (d) 384
  25. 25.What is the 35th term of the AP 7, 15, 23, 31, …? (a) 272 (b) 280 (c) 279 (d) 287
  26. 26.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 720 (b) 63 (c) 390 (d) 360
  27. 27.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 14 (b) 19 (c) 12 (d) 13
  28. 28.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 126 (c) 63 (d) 13
  29. 29.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 870 (d) 841
  30. 30.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 84 (c) 17 (d) 77
  31. 31.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 25 (c) 15 (d) 9
  32. 32.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 64 (b) 63 (c) 11 (d) 126
  33. 33.What is the 14th term of the AP 18, 27, 36, 45, …? (a) 135 (b) 144 (c) 126 (d) 117
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  35. 35.Which term of the AP 16, 25, 34, 43, … is 367? (a) 40th (b) 39th (c) 41st (d) 42nd
  36. 36.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2415 (c) 2416 (d) 2346
  37. 37.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 225 (c) 240 (d) 29
  38. 38.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 65 (b) 19 (c) 110 (d) 55
  39. 39.What is the missing term in the AP 7, 15, ?, 31, 39? (a) 24 (b) 23 (c) 22 (d) 31
  40. 40.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 21 (b) 22 (c) 23 (d) 27

Answer key

  1. 4005
  2. 26
  3. 15
  4. 4278
  5. 200
  6. 229
  7. 4851
  8. 181
  9. 100
  10. 257
  11. 154
  12. 158
  13. 314
  14. 301
  15. 231
  16. 150
  17. 38th
  18. 171
  19. 48
  20. 41
  21. 70
  22. 261
  23. 351
  24. 384
  25. 279
  26. 360
  27. 13
  28. 63
  29. 841
  30. 77
  31. 25
  32. 63
  33. 135
  34. 256
  35. 40th
  36. 2415
  37. 225
  38. 55
  39. 23
  40. 22

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