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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 648 · 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 8 terms of the AP 4, 9, 14, …? (a) 192 (b) 172 (c) 344 (d) 39
  2. 2.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 110 (b) 55 (c) 60 (d) 15
  3. 3.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 8372 (c) 4095 (d) 4186
  4. 4.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 171 (d) 35
  5. 5.What is the 29th term of the AP 19, 23, 27, 31, …? (a) 116 (b) 135 (c) 131 (d) 112
  6. 6.What is the 23rd term of the AP 17, 26, 35, 44, …? (a) 207 (b) 215 (c) 198 (d) 224
  7. 7.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 19 (b) 182 (c) 98 (d) 91
  8. 8.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 60 (c) 57 (d) 12
  9. 9.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  10. 10.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 36 (c) 15 (d) 72
  11. 11.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 408 (b) 378 (c) 756 (d) 59
  12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
  13. 13.What is the 37th term of the AP 11, 18, 25, 32, …? (a) 252 (b) 259 (c) 263 (d) 270
  14. 14.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 903 (c) 1892 (d) 947
  15. 15.Which term of the AP 18, 25, 32, 39, … is 200? (a) 29th (b) 28th (c) 27th (d) 26th
  16. 16.What is the 33rd term of the AP 11, 14, 17, 20, …? (a) 110 (b) 99 (c) 96 (d) 107
  17. 17.What is the 31st term of the AP 6, 13, 20, 27, …? (a) 216 (b) 210 (c) 223 (d) 217
  18. 18.What is the 27th term of the AP 13, 18, 23, 28, …? (a) 148 (b) 135 (c) 130 (d) 143
  19. 19.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 21 (b) 23 (c) 19 (d) 20
  20. 20.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 23 (b) 22 (c) 24 (d) 26
  21. 21.Which term of the AP 1, 7, 13, 19, … is 43? (a) 9th (b) 10th (c) 8th (d) 7th
  22. 22.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 30 (b) 144 (c) 256 (d) 128
  23. 23.What is the 10th term of the AP 18, 23, 28, 33, …? (a) 50 (b) 68 (c) 63 (d) 45
  24. 24.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 624 (b) 336 (c) 48 (d) 312
  25. 25.Which term of the AP 11, 15, 19, 23, … is 103? (a) 25th (b) 24th (c) 23rd (d) 26th
  26. 26.What is the 31st term of the AP 17, 25, 33, 41, …? (a) 257 (b) 240 (c) 265 (d) 248
  27. 27.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 47 (d) 300
  28. 28.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4371 (c) 4372 (d) 4278
  29. 29.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 900 (c) 59 (d) 930
  30. 30.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 20 (b) 154 (c) 77 (d) 80
  31. 31.What is the missing term in the AP 17, 22, 27, ?, 37? (a) 32 (b) 31 (c) 37 (d) 33
  32. 32.Which term of the AP 20, 27, 34, 41, … is 132? (a) 18th (b) 19th (c) 16th (d) 17th
  33. 33.What is the 35th term of the AP 15, 23, 31, 39, …? (a) 287 (b) 295 (c) 272 (d) 280
  34. 34.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
  36. 36.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 39 (b) 49 (c) 41 (d) 40
  37. 37.What is the 38th term of the AP 14, 17, 20, 23, …? (a) 114 (b) 128 (c) 125 (d) 111
  38. 38.What is the 30th term of the AP 1, 6, 11, 16, …? (a) 150 (b) 151 (c) 145 (d) 146
  39. 39.What is the 18th term of the AP 4, 7, 10, 13, …? (a) 51 (b) 54 (c) 55 (d) 58
  40. 40.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 90 (c) 180 (d) 13

Answer key

  1. 172
  2. 55
  3. 4186
  4. 324
  5. 131
  6. 215
  7. 91
  8. 57
  9. 441
  10. 64
  11. 378
  12. 784
  13. 263
  14. 946
  15. 27th
  16. 107
  17. 216
  18. 143
  19. 20
  20. 23
  21. 8th
  22. 128
  23. 63
  24. 312
  25. 24th
  26. 257
  27. 576
  28. 4371
  29. 900
  30. 77
  31. 32
  32. 17th
  33. 287
  34. 144
  35. 121
  36. 40
  37. 125
  38. 146
  39. 55
  40. 90

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