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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 946 · 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 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  2. 2.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 270 (b) 540 (c) 54 (d) 297
  3. 3.What is the 13th term of the AP 18, 21, 24, 27, …? (a) 57 (b) 36 (c) 39 (d) 54
  4. 4.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 13 (d) 49
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  6. 6.Which term of the AP 9, 13, 17, 21, … is 97? (a) 25th (b) 23rd (c) 24th (d) 22nd
  7. 7.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 13 (b) 12 (c) 11 (d) 15
  8. 8.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  9. 9.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 22 (b) 18 (c) 17 (d) 16
  10. 10.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 31 (b) 32 (c) 30 (d) 40
  11. 11.What is the 32nd term of the AP 2, 8, 14, 20, …? (a) 194 (b) 192 (c) 186 (d) 188
  12. 12.Which term of the AP 10, 17, 24, 31, … is 143? (a) 20th (b) 22nd (c) 19th (d) 21st
  13. 13.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 294 (b) 588 (c) 41 (d) 312
  14. 14.What is the 22nd term of the AP 19, 27, 35, 43, …? (a) 195 (b) 168 (c) 187 (d) 176
  15. 15.Which term of the AP 18, 21, 24, 27, … is 108? (a) 32nd (b) 31st (c) 36th (d) 30th
  16. 16.What is the 36th term of the AP 20, 27, 34, 41, …? (a) 272 (b) 265 (c) 252 (d) 245
  17. 17.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 10 (b) 8 (c) 12 (d) 9
  18. 18.What is the 39th term of the AP 11, 16, 21, 26, …? (a) 201 (b) 195 (c) 190 (d) 206
  19. 19.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 1711 (c) 1771 (d) 3540
  20. 20.What is the 22nd term of the AP 1, 3, 5, 7, …? (a) 42 (b) 44 (c) 43 (d) 45
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 121 (d) 21
  22. 22.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 50 (c) 13 (d) 45
  23. 23.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 12 (b) 10 (c) 11 (d) 15
  24. 24.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 128 (b) 64 (c) 72 (d) 15
  25. 25.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 6480 (c) 3160 (d) 3200
  26. 26.What is the 37th term of the AP 10, 16, 22, 28, …? (a) 222 (b) 216 (c) 226 (d) 232
  27. 27.What is the 14th term of the AP 12, 17, 22, 27, …? (a) 70 (b) 82 (c) 65 (d) 77
  28. 28.What is the 30th term of the AP 16, 19, 22, 25, …? (a) 106 (b) 87 (c) 103 (d) 90
  29. 29.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 26 (b) 24 (c) 25 (d) 32
  30. 30.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 406 (d) 812
  31. 31.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4371 (c) 4372 (d) 4278
  32. 32.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 384 (b) 720 (c) 52 (d) 360
  33. 33.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 380 (b) 190 (c) 28 (d) 200
  34. 34.What is the 20th term of the AP 10, 13, 16, 19, …? (a) 57 (b) 67 (c) 60 (d) 70
  35. 35.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 63 (b) 15 (c) 126 (d) 70
  36. 36.What is the 12th term of the AP 3, 6, 9, 12, …? (a) 39 (b) 33 (c) 37 (d) 36
  37. 37.What is the 16th term of the AP 16, 23, 30, 37, …? (a) 128 (b) 105 (c) 112 (d) 121
  38. 38.What is the 35th term of the AP 6, 8, 10, 12, …? (a) 76 (b) 68 (c) 70 (d) 74
  39. 39.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 253 (b) 38 (c) 506 (d) 256
  40. 40.What is the 35th term of the AP 6, 10, 14, 18, …? (a) 136 (b) 146 (c) 140 (d) 142

Answer key

  1. 625
  2. 270
  3. 54
  4. 49
  5. 100
  6. 23rd
  7. 12
  8. 729
  9. 17
  10. 31
  11. 188
  12. 20th
  13. 294
  14. 187
  15. 31st
  16. 265
  17. 9
  18. 201
  19. 1770
  20. 43
  21. 121
  22. 45
  23. 11
  24. 64
  25. 3240
  26. 226
  27. 77
  28. 103
  29. 25
  30. 406
  31. 4371
  32. 360
  33. 190
  34. 67
  35. 63
  36. 36
  37. 121
  38. 74
  39. 253
  40. 142

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