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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 864 · 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 11th term of the AP 10, 16, 22, 28, …? (a) 66 (b) 76 (c) 70 (d) 60
  2. 2.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 198 (b) 360 (c) 180 (d) 36
  3. 3.What is the 17th term of the AP 7, 9, 11, 13, …? (a) 34 (b) 41 (c) 39 (d) 32
  4. 4.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 18 (b) 17 (c) 19 (d) 16
  5. 5.Which term of the AP 4, 8, 12, 16, … is 44? (a) 12th (b) 11th (c) 10th (d) 13th
  6. 6.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 9506 (c) 4754 (d) 4753
  7. 7.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3828 (c) 3872 (d) 3916
  8. 8.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 363 (c) 726 (d) 58
  9. 9.What is the 29th term of the AP 2, 10, 18, 26, …? (a) 234 (b) 224 (c) 232 (d) 226
  10. 10.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 22 (b) 182 (c) 94 (d) 91
  11. 11.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 15 (b) 16 (c) 21 (d) 17
  12. 12.What is the 29th term of the AP 4, 10, 16, 22, …? (a) 168 (b) 174 (c) 178 (d) 172
  13. 13.What is the missing term in the AP 2, 9, 16, ?, 30? (a) 24 (b) 22 (c) 30 (d) 23
  14. 14.What is the 27th term of the AP 7, 13, 19, 25, …? (a) 163 (b) 169 (c) 156 (d) 162
  15. 15.What is the 23rd term of the AP 20, 22, 24, 26, …? (a) 44 (b) 46 (c) 66 (d) 64
  16. 16.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  17. 17.Which term of the AP 3, 7, 11, 15, … is 123? (a) 30th (b) 31st (c) 33rd (d) 32nd
  18. 18.What is the 14th term of the AP 1, 8, 15, 22, …? (a) 92 (b) 98 (c) 91 (d) 99
  19. 19.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 28 (b) 27 (c) 26 (d) 35
  20. 20.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 85 (b) 26 (c) 70 (d) 140
  21. 21.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 480 (b) 252 (c) 31 (d) 240
  22. 22.What is the 18th term of the AP 19, 22, 25, 28, …? (a) 73 (b) 54 (c) 70 (d) 51
  23. 23.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 32 (b) 40 (c) 30 (d) 31
  24. 24.What is the 26th term of the AP 10, 17, 24, 31, …? (a) 182 (b) 185 (c) 175 (d) 192
  25. 25.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 444 (b) 62 (c) 414 (d) 828
  26. 26.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  27. 27.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 378 (b) 33 (c) 189 (d) 192
  28. 28.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 406 (d) 812
  29. 29.Which term of the AP 1, 5, 9, 13, … is 29? (a) 7th (b) 9th (c) 10th (d) 8th
  30. 30.What is the 21st term of the AP 5, 12, 19, 26, …? (a) 147 (b) 140 (c) 152 (d) 145
  31. 31.What is the 12th term of the AP 2, 6, 10, 14, …? (a) 50 (b) 44 (c) 48 (d) 46
  32. 32.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 23 (b) 21 (c) 30 (d) 22
  33. 33.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 21 (b) 19 (c) 18 (d) 20
  34. 34.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 10100 (c) 5000 (d) 5050
  35. 35.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 72 (b) 80 (c) 144 (d) 16
  36. 36.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 49 (b) 248 (c) 448 (d) 224
  37. 37.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 8 (b) 11 (c) 9 (d) 7
  38. 38.What is the 13th term of the AP 19, 26, 33, 40, …? (a) 103 (b) 84 (c) 91 (d) 110
  39. 39.Which term of the AP 20, 25, 30, 35, … is 200? (a) 40th (b) 37th (c) 36th (d) 38th
  40. 40.What is the sum of all the whole numbers from 1 to 92? (a) 4186 (b) 4232 (c) 4278 (d) 8556

Answer key

  1. 70
  2. 180
  3. 39
  4. 17
  5. 11th
  6. 4753
  7. 3916
  8. 363
  9. 226
  10. 91
  11. 16
  12. 172
  13. 23
  14. 163
  15. 64
  16. 400
  17. 31st
  18. 92
  19. 27
  20. 70
  21. 240
  22. 70
  23. 31
  24. 185
  25. 414
  26. 441
  27. 189
  28. 784
  29. 8th
  30. 145
  31. 46
  32. 22
  33. 19
  34. 5050
  35. 72
  36. 224
  37. 8
  38. 103
  39. 37th
  40. 4278

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