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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 306 · 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 6 terms of the AP 10, 12, 14, …? (a) 180 (b) 96 (c) 20 (d) 90
  2. 2.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 30 (d) 9
  3. 3.Which term of the AP 7, 12, 17, 22, … is 132? (a) 25th (b) 27th (c) 28th (d) 26th
  4. 4.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 22 (b) 20 (c) 21 (d) 28
  5. 5.What is the 37th term of the AP 13, 16, 19, 22, …? (a) 124 (b) 121 (c) 111 (d) 108
  6. 6.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 52 (b) 384 (c) 360 (d) 720
  7. 7.Which term of the AP 20, 28, 36, 44, … is 204? (a) 25th (b) 23rd (c) 24th (d) 26th
  8. 8.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 15 (b) 7 (c) 8 (d) 9
  9. 9.What is the 27th term of the AP 1, 10, 19, 28, …? (a) 244 (b) 234 (c) 243 (d) 235
  10. 10.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 780 (c) 1640 (d) 800
  11. 11.What is the 33rd term of the AP 14, 23, 32, 41, …? (a) 311 (b) 302 (c) 297 (d) 288
  12. 12.What is the 28th term of the AP 19, 21, 23, 25, …? (a) 73 (b) 56 (c) 54 (d) 75
  13. 13.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 18 (b) 11 (c) 12 (d) 13
  14. 14.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 162 (b) 81 (c) 13 (d) 82
  15. 15.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 256 (d) 272
  16. 16.What is the sum of all the whole numbers from 1 to 72? (a) 2628 (b) 5256 (c) 2556 (d) 2592
  17. 17.What is the 17th term of the AP 8, 14, 20, 26, …? (a) 104 (b) 110 (c) 96 (d) 102
  18. 18.What is the 12th term of the AP 2, 10, 18, 26, …? (a) 88 (b) 98 (c) 90 (d) 96
  19. 19.Which term of the AP 17, 24, 31, 38, … is 164? (a) 23rd (b) 22nd (c) 24th (d) 21st
  20. 20.What is the 14th term of the AP 7, 10, 13, 16, …? (a) 39 (b) 42 (c) 46 (d) 49
  21. 21.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 440 (b) 240 (c) 220 (d) 45
  22. 22.What is the 39th term of the AP 18, 22, 26, 30, …? (a) 174 (b) 152 (c) 156 (d) 170
  23. 23.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1352 (c) 1326 (d) 1378
  24. 24.Which term of the AP 3, 10, 17, 24, … is 248? (a) 38th (b) 36th (c) 35th (d) 37th
  25. 25.What is the 16th term of the AP 20, 25, 30, 35, …? (a) 75 (b) 95 (c) 80 (d) 100
  26. 26.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 19 (b) 20 (c) 24 (d) 21
  27. 27.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 351 (c) 702 (d) 338
  28. 28.Which term of the AP 4, 6, 8, 10, … is 38? (a) 17th (b) 20th (c) 18th (d) 19th
  29. 29.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 12 (b) 14 (c) 11 (d) 10
  30. 30.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 378 (b) 45 (c) 210 (d) 189
  31. 31.Which term of the AP 16, 24, 32, 40, … is 72? (a) 8th (b) 9th (c) 10th (d) 7th
  32. 32.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 228 (b) 420 (c) 210 (d) 34
  33. 33.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 294 (b) 312 (c) 41 (d) 588
  34. 34.What is the 39th term of the AP 10, 18, 26, 34, …? (a) 304 (b) 314 (c) 312 (d) 322
  35. 35.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2016 (c) 2048 (d) 2080
  36. 36.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 210 (d) 420
  37. 37.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 35 (c) 70 (d) 40
  38. 38.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 16 (b) 14 (c) 22 (d) 15
  39. 39.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 8 (b) 10 (c) 17 (d) 9
  40. 40.What is the 22nd term of the AP 1, 3, 5, 7, …? (a) 42 (b) 45 (c) 43 (d) 44

Answer key

  1. 90
  2. 25
  3. 26th
  4. 21
  5. 121
  6. 360
  7. 24th
  8. 8
  9. 235
  10. 820
  11. 302
  12. 73
  13. 12
  14. 81
  15. 256
  16. 2628
  17. 104
  18. 90
  19. 22nd
  20. 46
  21. 220
  22. 170
  23. 1378
  24. 36th
  25. 95
  26. 20
  27. 351
  28. 18th
  29. 11
  30. 189
  31. 8th
  32. 210
  33. 294
  34. 314
  35. 2080
  36. 400
  37. 35
  38. 15
  39. 9
  40. 43

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