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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 766 · 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 12 terms of the AP 9, 10, 11, …? (a) 174 (b) 20 (c) 180 (d) 348
  2. 2.What is the 15th term of the AP 14, 23, 32, 41, …? (a) 149 (b) 135 (c) 126 (d) 140
  3. 3.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 127 (b) 126 (c) 252 (d) 18
  4. 4.Which term of the AP 5, 14, 23, 32, … is 167? (a) 18th (b) 20th (c) 19th (d) 21st
  5. 5.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 22 (b) 21 (c) 24 (d) 23
  6. 6.What is the sum of all the whole numbers from 1 to 67? (a) 2279 (b) 2278 (c) 2211 (d) 4556
  7. 7.What is the missing term in the AP 18, 24, 30, ?, 42? (a) 42 (b) 35 (c) 37 (d) 36
  8. 8.What is the 12th term of the AP 18, 22, 26, 30, …? (a) 66 (b) 48 (c) 44 (d) 62
  9. 9.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 54 (b) 13 (c) 96 (d) 48
  10. 10.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 756 (c) 378 (d) 351
  11. 11.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 320 (b) 56 (c) 290 (d) 580
  12. 12.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 118 (c) 117 (d) 17
  13. 13.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 13 (b) 18 (c) 14 (d) 15
  14. 14.Which term of the AP 11, 14, 17, 20, … is 59? (a) 17th (b) 18th (c) 16th (d) 19th
  15. 15.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 150 (b) 168 (c) 300 (d) 40
  16. 16.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 75 (c) 78 (d) 150
  17. 17.Which term of the AP 5, 7, 9, 11, … is 27? (a) 14th (b) 12th (c) 13th (d) 11th
  18. 18.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 84 (b) 90 (c) 19 (d) 168
  19. 19.Which term of the AP 17, 24, 31, 38, … is 262? (a) 35th (b) 37th (c) 38th (d) 36th
  20. 20.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 15 (b) 8 (c) 10 (d) 9
  21. 21.What is the 24th term of the AP 12, 15, 18, 21, …? (a) 84 (b) 81 (c) 69 (d) 72
  22. 22.What is the 18th term of the AP 6, 14, 22, 30, …? (a) 144 (b) 150 (c) 142 (d) 136
  23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 225 (d) 120
  24. 24.Which term of the AP 3, 8, 13, 18, … is 58? (a) 14th (b) 11th (c) 13th (d) 12th
  25. 25.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 600 (d) 576
  26. 26.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 408 (b) 54 (c) 384 (d) 768
  27. 27.What is the missing term in the AP 9, 17, 25, ?, 41? (a) 41 (b) 34 (c) 32 (d) 33
  28. 28.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 223 (b) 440 (c) 220 (d) 35
  29. 29.What is the missing term in the AP 2, 10, ?, 26, 34? (a) 18 (b) 17 (c) 26 (d) 19
  30. 30.What is the 39th term of the AP 11, 17, 23, 29, …? (a) 245 (b) 228 (c) 234 (d) 239
  31. 31.Which term of the AP 11, 15, 19, 23, … is 151? (a) 36th (b) 38th (c) 37th (d) 35th
  32. 32.What is the 20th term of the AP 12, 17, 22, 27, …? (a) 112 (b) 100 (c) 107 (d) 95
  33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  34. 34.What is the 29th term of the AP 18, 26, 34, 42, …? (a) 250 (b) 242 (c) 224 (d) 232
  35. 35.What is the 35th term of the AP 19, 22, 25, 28, …? (a) 124 (b) 102 (c) 105 (d) 121
  36. 36.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 49 (b) 10 (c) 98 (d) 50
  37. 37.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 235 (b) 470 (c) 46 (d) 260
  38. 38.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 19 (b) 18 (c) 17 (d) 20
  39. 39.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 308 (b) 286 (c) 46 (d) 572
  40. 40.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 2162 (c) 1081 (d) 1058

Answer key

  1. 174
  2. 140
  3. 126
  4. 19th
  5. 22
  6. 2278
  7. 36
  8. 62
  9. 48
  10. 378
  11. 290
  12. 117
  13. 14
  14. 17th
  15. 150
  16. 75
  17. 12th
  18. 84
  19. 36th
  20. 9
  21. 81
  22. 142
  23. 225
  24. 12th
  25. 576
  26. 384
  27. 33
  28. 220
  29. 18
  30. 239
  31. 36th
  32. 107
  33. 25
  34. 242
  35. 121
  36. 49
  37. 235
  38. 18
  39. 286
  40. 1081

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