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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 424 · 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 missing term in the AP 12, ?, 24, 30, 36? (a) 24 (b) 17 (c) 19 (d) 18
  2. 2.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 124 (b) 26 (c) 248 (d) 136
  3. 3.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2016 (c) 2080 (d) 4160
  4. 4.Which term of the AP 18, 25, 32, 39, … is 200? (a) 27th (b) 29th (c) 28th (d) 26th
  5. 5.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 820 (c) 780 (d) 1640
  6. 6.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 184 (b) 44 (c) 208 (d) 368
  7. 7.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 31 (b) 152 (c) 136 (d) 272
  8. 8.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 22 (b) 19 (c) 17 (d) 18
  9. 9.What is the 28th term of the AP 13, 18, 23, 28, …? (a) 135 (b) 148 (c) 140 (d) 153
  10. 10.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4951 (c) 4950 (d) 4851
  11. 11.What is the 38th term of the AP 5, 14, 23, 32, …? (a) 347 (b) 342 (c) 333 (d) 338
  12. 12.Which term of the AP 9, 16, 23, 30, … is 86? (a) 12th (b) 14th (c) 11th (d) 13th
  13. 13.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 35 (d) 342
  14. 14.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4465 (c) 4418 (d) 4371
  15. 15.What is the 15th term of the AP 18, 23, 28, 33, …? (a) 88 (b) 75 (c) 93 (d) 70
  16. 16.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 15 (b) 12 (c) 13 (d) 11
  17. 17.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 38 (b) 208 (c) 192 (d) 384
  18. 18.Which term of the AP 17, 21, 25, 29, … is 81? (a) 17th (b) 16th (c) 18th (d) 19th
  19. 19.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 164 (b) 328 (c) 38 (d) 184
  20. 20.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 13 (b) 15 (c) 11 (d) 12
  21. 21.Which term of the AP 15, 19, 23, 27, … is 99? (a) 24th (b) 23rd (c) 22nd (d) 21st
  22. 22.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 756 (c) 53 (d) 378
  23. 23.What is the 35th term of the AP 13, 17, 21, 25, …? (a) 149 (b) 153 (c) 140 (d) 136
  24. 24.What is the 17th term of the AP 3, 5, 7, 9, …? (a) 34 (b) 35 (c) 37 (d) 32
  25. 25.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 420 (b) 230 (c) 39 (d) 210
  26. 26.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 21 (b) 20 (c) 29 (d) 22
  27. 27.What is the 16th term of the AP 3, 10, 17, 24, …? (a) 115 (b) 105 (c) 108 (d) 112
  28. 28.What is the 17th term of the AP 11, 13, 15, 17, …? (a) 45 (b) 43 (c) 32 (d) 34
  29. 29.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 19 (b) 16 (c) 17 (d) 15
  30. 30.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 225 (b) 450 (c) 243 (d) 41
  31. 31.What is the sum of all the whole numbers from 1 to 20? (a) 190 (b) 420 (c) 200 (d) 210
  32. 32.Which term of the AP 3, 9, 15, 21, … is 183? (a) 33rd (b) 31st (c) 32nd (d) 30th
  33. 33.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 23 (b) 196 (c) 101 (d) 98
  34. 34.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 1332 (c) 648 (d) 666
  35. 35.Which term of the AP 2, 6, 10, 14, … is 98? (a) 24th (b) 27th (c) 25th (d) 26th
  36. 36.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 253 (d) 484
  37. 37.What is the 36th term of the AP 1, 4, 7, 10, …? (a) 106 (b) 109 (c) 108 (d) 105
  38. 38.Which term of the AP 11, 17, 23, 29, … is 149? (a) 25th (b) 23rd (c) 26th (d) 24th
  39. 39.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 18 (b) 11 (c) 10 (d) 9
  40. 40.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 126 (b) 28 (c) 112 (d) 224

Answer key

  1. 18
  2. 124
  3. 2080
  4. 27th
  5. 820
  6. 184
  7. 136
  8. 18
  9. 148
  10. 4950
  11. 338
  12. 12th
  13. 324
  14. 4465
  15. 88
  16. 12
  17. 192
  18. 17th
  19. 164
  20. 12
  21. 22nd
  22. 729
  23. 149
  24. 35
  25. 210
  26. 21
  27. 108
  28. 43
  29. 16
  30. 225
  31. 210
  32. 31st
  33. 98
  34. 666
  35. 25th
  36. 484
  37. 106
  38. 24th
  39. 10
  40. 112

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