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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 410 · 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 9 terms of the AP 7, 10, 13, …? (a) 174 (b) 31 (c) 171 (d) 342
  2. 2.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 312 (b) 176 (c) 156 (d) 37
  3. 3.What is the missing term in the AP 18, ?, 28, 33, 38? (a) 24 (b) 28 (c) 23 (d) 22
  4. 4.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 28 (b) 160 (c) 95 (d) 80
  5. 5.What is the 30th term of the AP 3, 6, 9, 12, …? (a) 87 (b) 93 (c) 91 (d) 90
  6. 6.What is the 14th term of the AP 20, 28, 36, 44, …? (a) 104 (b) 112 (c) 132 (d) 124
  7. 7.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 8 (b) 7 (c) 9 (d) 10
  8. 8.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 420 (d) 400
  9. 9.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 84 (b) 150 (c) 20 (d) 75
  10. 10.What is the 28th term of the AP 9, 14, 19, 24, …? (a) 144 (b) 140 (c) 149 (d) 135
  11. 11.What is the sum of all the whole numbers from 1 to 72? (a) 2628 (b) 5256 (c) 2592 (d) 2556
  12. 12.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 24 (b) 26 (c) 25 (d) 32
  13. 13.What is the sum of all the whole numbers from 1 to 76? (a) 2926 (b) 5852 (c) 2888 (d) 2850
  14. 14.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 3916 (c) 4005 (d) 4006
  15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 870 (d) 57
  16. 16.What is the 21st term of the AP 7, 9, 11, 13, …? (a) 40 (b) 47 (c) 42 (d) 49
  17. 17.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 616 (b) 308 (c) 48 (d) 330
  18. 18.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 300 (b) 276 (c) 552 (d) 45
  19. 19.Which term of the AP 13, 15, 17, 19, … is 81? (a) 35th (b) 37th (c) 34th (d) 36th
  20. 20.Which term of the AP 10, 12, 14, 16, … is 32? (a) 11th (b) 13th (c) 12th (d) 16th
  21. 21.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 50 (b) 100 (c) 16 (d) 53
  22. 22.What is the 17th term of the AP 13, 22, 31, 40, …? (a) 166 (b) 144 (c) 153 (d) 157
  23. 23.What is the 35th term of the AP 4, 6, 8, 10, …? (a) 74 (b) 70 (c) 68 (d) 72
  24. 24.What is the 34th term of the AP 8, 12, 16, 20, …? (a) 140 (b) 144 (c) 132 (d) 136
  25. 25.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 4186 (c) 8372 (d) 4187
  26. 26.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 21 (b) 55 (c) 110 (d) 60
  27. 27.Which term of the AP 9, 14, 19, 24, … is 189? (a) 36th (b) 38th (c) 39th (d) 37th
  28. 28.Which term of the AP 10, 17, 24, 31, … is 269? (a) 37th (b) 40th (c) 39th (d) 38th
  29. 29.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 289 (d) 153
  30. 30.What is the missing term in the AP 19, 28, ?, 46, 55? (a) 38 (b) 46 (c) 37 (d) 36
  31. 31.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 19 (b) 138 (c) 69 (d) 78
  32. 32.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 3042 (c) 6162 (d) 3081
  33. 33.Which term of the AP 11, 13, 15, 17, … is 53? (a) 24th (b) 23rd (c) 22nd (d) 21st
  34. 34.Which term of the AP 4, 6, 8, 10, … is 18? (a) 9th (b) 7th (c) 8th (d) 10th
  35. 35.What is the 34th term of the AP 10, 17, 24, 31, …? (a) 248 (b) 231 (c) 241 (d) 238
  36. 36.What is the missing term in the AP 16, 23, ?, 37, 44? (a) 30 (b) 31 (c) 37 (d) 29
  37. 37.What is the 26th term of the AP 18, 26, 34, 42, …? (a) 208 (b) 218 (c) 200 (d) 226
  38. 38.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 13 (d) 49
  39. 39.What is the 11th term of the AP 6, 9, 12, 15, …? (a) 30 (b) 39 (c) 33 (d) 36
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 11 (d) 21

Answer key

  1. 171
  2. 156
  3. 23
  4. 80
  5. 90
  6. 124
  7. 8
  8. 400
  9. 75
  10. 144
  11. 2628
  12. 25
  13. 2926
  14. 4005
  15. 841
  16. 47
  17. 308
  18. 276
  19. 35th
  20. 12th
  21. 50
  22. 157
  23. 72
  24. 140
  25. 4186
  26. 55
  27. 37th
  28. 38th
  29. 289
  30. 37
  31. 69
  32. 3081
  33. 22nd
  34. 8th
  35. 241
  36. 30
  37. 218
  38. 49
  39. 36
  40. 36

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