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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 966 · 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 5 terms of the AP 6, 12, 18, …? (a) 180 (b) 105 (c) 30 (d) 90
  2. 2.Which term of the AP 1, 6, 11, 16, … is 86? (a) 19th (b) 17th (c) 20th (d) 18th
  3. 3.What is the 17th term of the AP 11, 16, 21, 26, …? (a) 80 (b) 91 (c) 96 (d) 85
  4. 4.What is the 13th term of the AP 18, 21, 24, 27, …? (a) 39 (b) 57 (c) 36 (d) 54
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 56 (d) 13
  6. 6.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1128 (c) 1081 (d) 2256
  7. 7.What is the 32nd term of the AP 2, 10, 18, 26, …? (a) 248 (b) 250 (c) 256 (d) 258
  8. 8.What is the 13th term of the AP 5, 7, 9, 11, …? (a) 26 (b) 29 (c) 24 (d) 31
  9. 9.What is the 28th term of the AP 7, 13, 19, 25, …? (a) 169 (b) 168 (c) 162 (d) 175
  10. 10.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 352 (b) 36 (c) 192 (d) 176
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  12. 12.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 24 (b) 26 (c) 30 (d) 25
  13. 13.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 27 (b) 174 (c) 102 (d) 87
  14. 14.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 24 (b) 25 (c) 26 (d) 29
  15. 15.Which term of the AP 4, 9, 14, 19, … is 129? (a) 25th (b) 28th (c) 27th (d) 26th
  16. 16.What is the missing term in the AP 8, 16, 24, ?, 40? (a) 33 (b) 31 (c) 40 (d) 32
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 153 (c) 33 (d) 306
  18. 18.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3321 (c) 6642 (d) 3322
  19. 19.What is the 33rd term of the AP 20, 22, 24, 26, …? (a) 84 (b) 66 (c) 64 (d) 86
  20. 20.What is the 17th term of the AP 18, 20, 22, 24, …? (a) 32 (b) 52 (c) 50 (d) 34
  21. 21.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2485 (c) 2557 (d) 5112
  22. 22.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 38 (b) 31 (c) 33 (d) 32
  23. 23.What is the 29th term of the AP 18, 25, 32, 39, …? (a) 203 (b) 221 (c) 196 (d) 214
  24. 24.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 171 (b) 35 (c) 189 (d) 342
  25. 25.What is the 13th term of the AP 8, 17, 26, 35, …? (a) 108 (b) 125 (c) 117 (d) 116
  26. 26.Which term of the AP 7, 11, 15, 19, … is 51? (a) 11th (b) 14th (c) 13th (d) 12th
  27. 27.What is the 32nd term of the AP 9, 12, 15, 18, …? (a) 102 (b) 93 (c) 105 (d) 96
  28. 28.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3528 (c) 3486 (d) 3570
  29. 29.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 6806 (c) 3321 (d) 3362
  30. 30.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 15 (d) 25
  31. 31.What is the 28th term of the AP 11, 20, 29, 38, …? (a) 263 (b) 252 (c) 254 (d) 243
  32. 32.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 6 (b) 7 (c) 11 (d) 8
  33. 33.What is the 28th term of the AP 13, 22, 31, 40, …? (a) 243 (b) 265 (c) 252 (d) 256
  34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 756 (d) 729
  35. 35.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 456 (b) 63 (c) 426 (d) 852
  36. 36.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 350 (b) 175 (c) 196 (d) 43
  37. 37.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 33 (b) 43 (c) 35 (d) 34
  38. 38.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 294 (b) 147 (c) 39 (d) 168
  39. 39.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 110 (d) 100
  40. 40.What is the 19th term of the AP 4, 9, 14, 19, …? (a) 99 (b) 94 (c) 95 (d) 90

Answer key

  1. 90
  2. 18th
  3. 91
  4. 54
  5. 49
  6. 1128
  7. 250
  8. 29
  9. 169
  10. 176
  11. 144
  12. 25
  13. 87
  14. 25
  15. 26th
  16. 32
  17. 289
  18. 3321
  19. 84
  20. 50
  21. 2556
  22. 32
  23. 214
  24. 171
  25. 116
  26. 12th
  27. 102
  28. 3570
  29. 3403
  30. 25
  31. 254
  32. 7
  33. 256
  34. 729
  35. 426
  36. 175
  37. 34
  38. 147
  39. 100
  40. 94

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