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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 98 · 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 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 19 (d) 55
  2. 2.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 264 (c) 150 (d) 132
  3. 3.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 200 (b) 180 (c) 360 (d) 40
  4. 4.What is the 31st term of the AP 14, 22, 30, 38, …? (a) 248 (b) 240 (c) 262 (d) 254
  5. 5.What is the 14th term of the AP 14, 18, 22, 26, …? (a) 70 (b) 66 (c) 52 (d) 56
  6. 6.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 78 (c) 182 (d) 91
  7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 56 (d) 49
  8. 8.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 380 (b) 190 (c) 37 (d) 210
  9. 9.Which term of the AP 3, 9, 15, 21, … is 219? (a) 37th (b) 39th (c) 36th (d) 38th
  10. 10.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 168 (b) 312 (c) 30 (d) 156
  11. 11.Which term of the AP 18, 20, 22, 24, … is 66? (a) 33rd (b) 25th (c) 26th (d) 24th
  12. 12.What is the 38th term of the AP 3, 7, 11, 15, …? (a) 155 (b) 148 (c) 152 (d) 151
  13. 13.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2592 (c) 2628 (d) 2556
  14. 14.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  15. 15.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 128 (b) 256 (c) 144 (d) 30
  16. 16.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 78 (d) 144
  17. 17.What is the 19th term of the AP 2, 4, 6, 8, …? (a) 36 (b) 39 (c) 40 (d) 38
  18. 18.What is the 25th term of the AP 2, 9, 16, 23, …? (a) 177 (b) 168 (c) 175 (d) 170
  19. 19.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 272 (d) 136
  20. 20.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 1806 (c) 861 (d) 903
  21. 21.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 108 (b) 109 (c) 16 (d) 216
  22. 22.What is the missing term in the AP 13, 21, ?, 37, 45? (a) 29 (b) 28 (c) 30 (d) 37
  23. 23.What is the 15th term of the AP 2, 11, 20, 29, …? (a) 126 (b) 137 (c) 128 (d) 135
  24. 24.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 330 (b) 352 (c) 50 (d) 660
  25. 25.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 16 (b) 21 (c) 17 (d) 15
  26. 26.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 504 (b) 52 (c) 279 (d) 252
  27. 27.What is the 25th term of the AP 4, 7, 10, 13, …? (a) 79 (b) 76 (c) 75 (d) 72
  28. 28.What is the 37th term of the AP 13, 20, 27, 34, …? (a) 272 (b) 265 (c) 252 (d) 259
  29. 29.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 28 (b) 27 (c) 26 (d) 34
  30. 30.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 42 (d) 21
  31. 31.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4851 (c) 4753 (d) 4802
  32. 32.What is the 34th term of the AP 2, 11, 20, 29, …? (a) 306 (b) 308 (c) 299 (d) 297
  33. 33.What is the missing term in the AP 15, ?, 19, 21, 23? (a) 17 (b) 16 (c) 19 (d) 18
  34. 34.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 253 (c) 277 (d) 276
  35. 35.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 156 (c) 78 (d) 72
  36. 36.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 465 (c) 496 (d) 497
  37. 37.What is the 10th term of the AP 18, 26, 34, 42, …? (a) 90 (b) 98 (c) 80 (d) 72
  38. 38.What is the 31st term of the AP 6, 13, 20, 27, …? (a) 223 (b) 217 (c) 216 (d) 210
  39. 39.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 444 (b) 816 (c) 408 (d) 67
  40. 40.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 204 (b) 102 (c) 120 (d) 32

Answer key

  1. 100
  2. 132
  3. 180
  4. 254
  5. 66
  6. 91
  7. 49
  8. 190
  9. 37th
  10. 156
  11. 25th
  12. 151
  13. 2628
  14. 625
  15. 128
  16. 144
  17. 38
  18. 170
  19. 256
  20. 903
  21. 108
  22. 29
  23. 128
  24. 330
  25. 16
  26. 252
  27. 76
  28. 265
  29. 27
  30. 36
  31. 4851
  32. 299
  33. 17
  34. 276
  35. 78
  36. 496
  37. 90
  38. 216
  39. 408
  40. 102

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