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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 874 · 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 19, 27, 35, 43, … is 195? (a) 25th (b) 23rd (c) 22nd (d) 24th
  2. 2.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 40 (b) 175 (c) 154 (d) 308
  3. 3.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 496 (c) 512 (d) 528
  4. 4.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 250 (b) 270 (c) 500 (d) 43
  5. 5.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 12 (c) 114 (d) 57
  6. 6.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 91 (b) 92 (c) 16 (d) 182
  7. 7.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
  8. 8.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 10 (c) 40 (d) 41
  9. 9.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 253 (c) 276 (d) 277
  10. 10.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4465 (c) 4561 (d) 4560
  11. 11.What is the 23rd term of the AP 10, 18, 26, 34, …? (a) 176 (b) 184 (c) 194 (d) 186
  12. 12.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  13. 13.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 27 (b) 29 (c) 26 (d) 25
  14. 14.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5000 (c) 10100 (d) 5050
  15. 15.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 150 (b) 75 (c) 90 (d) 27
  16. 16.What is the 20th term of the AP 15, 22, 29, 36, …? (a) 140 (b) 155 (c) 133 (d) 148
  17. 17.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 3540 (c) 1711 (d) 1770
  18. 18.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 220 (b) 38 (c) 400 (d) 200
  19. 19.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 300 (d) 576
  20. 20.What is the 30th term of the AP 6, 10, 14, 18, …? (a) 120 (b) 126 (c) 116 (d) 122
  21. 21.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 6642 (c) 3321 (d) 3322
  22. 22.What is the 10th term of the AP 15, 17, 19, 21, …? (a) 35 (b) 33 (c) 20 (d) 18
  23. 23.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 33 (b) 66 (c) 36 (d) 8
  24. 24.Which term of the AP 15, 21, 27, 33, … is 159? (a) 26th (b) 24th (c) 27th (d) 25th
  25. 25.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 108 (b) 10 (c) 55 (d) 54
  26. 26.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 33 (b) 26 (c) 27 (d) 28
  27. 27.Which term of the AP 1, 6, 11, 16, … is 106? (a) 22nd (b) 24th (c) 21st (d) 23rd
  28. 28.Which term of the AP 14, 17, 20, 23, … is 104? (a) 31st (b) 30th (c) 33rd (d) 32nd
  29. 29.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 115 (b) 120 (c) 230 (d) 16
  30. 30.What is the missing term in the AP 5, ?, 21, 29, 37? (a) 14 (b) 21 (c) 12 (d) 13
  31. 31.What is the 36th term of the AP 2, 6, 10, 14, …? (a) 140 (b) 146 (c) 142 (d) 144
  32. 32.What is the 10th term of the AP 6, 12, 18, 24, …? (a) 60 (b) 66 (c) 54 (d) 61
  33. 33.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 2450 (c) 2485 (d) 4970
  34. 34.What is the 34th term of the AP 15, 19, 23, 27, …? (a) 147 (b) 132 (c) 151 (d) 136
  35. 35.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 29 (b) 133 (c) 119 (d) 238
  36. 36.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 18 (b) 16 (c) 22 (d) 17
  37. 37.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 420 (d) 400
  38. 38.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 21 (b) 87 (c) 168 (d) 84
  39. 39.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 165 (b) 24 (c) 154 (d) 308
  40. 40.What is the missing term in the AP 20, 25, 30, ?, 40? (a) 40 (b) 35 (c) 34 (d) 36

Answer key

  1. 23rd
  2. 154
  3. 528
  4. 250
  5. 57
  6. 91
  7. 900
  8. 40
  9. 276
  10. 4560
  11. 186
  12. 841
  13. 26
  14. 5050
  15. 75
  16. 148
  17. 1770
  18. 200
  19. 576
  20. 122
  21. 3321
  22. 33
  23. 33
  24. 25th
  25. 54
  26. 27
  27. 22nd
  28. 31st
  29. 115
  30. 13
  31. 142
  32. 60
  33. 2485
  34. 147
  35. 119
  36. 17
  37. 400
  38. 84
  39. 154
  40. 35

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