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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 944 · 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 all the whole numbers from 1 to 85? (a) 7310 (b) 3656 (c) 3570 (d) 3655
  2. 2.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 37 (b) 36 (c) 45 (d) 35
  3. 3.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4095 (c) 8372 (d) 4186
  4. 4.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 360 (b) 60 (c) 660 (d) 330
  5. 5.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 28 (b) 21 (c) 22 (d) 20
  6. 6.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 196 (b) 105 (c) 98 (d) 20
  7. 7.What is the 14th term of the AP 12, 19, 26, 33, …? (a) 91 (b) 110 (c) 98 (d) 103
  8. 8.What is the 35th term of the AP 19, 22, 25, 28, …? (a) 102 (b) 124 (c) 121 (d) 105
  9. 9.Which term of the AP 20, 25, 30, 35, … is 165? (a) 29th (b) 30th (c) 33rd (d) 31st
  10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 21 (d) 36
  11. 11.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 25 (b) 27 (c) 26 (d) 34
  12. 12.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 224 (b) 448 (c) 248 (d) 49
  13. 13.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 406 (c) 436 (d) 435
  14. 14.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 22 (b) 132 (c) 143 (d) 264
  15. 15.What is the missing term in the AP 11, ?, 29, 38, 47? (a) 29 (b) 21 (c) 20 (d) 19
  16. 16.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 19 (b) 16 (c) 15 (d) 14
  17. 17.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 190 (b) 110 (c) 95 (d) 31
  18. 18.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1378 (c) 1431 (d) 1432
  19. 19.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 380 (b) 37 (c) 190 (d) 210
  20. 20.Which term of the AP 15, 23, 31, 39, … is 303? (a) 36th (b) 38th (c) 37th (d) 39th
  21. 21.What is the 14th term of the AP 3, 6, 9, 12, …? (a) 45 (b) 39 (c) 42 (d) 43
  22. 22.What is the 24th term of the AP 3, 11, 19, 27, …? (a) 195 (b) 187 (c) 184 (d) 192
  23. 23.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 25 (b) 30 (c) 50 (d) 9
  24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 420 (d) 39
  25. 25.What is the 40th term of the AP 2, 9, 16, 23, …? (a) 282 (b) 280 (c) 275 (d) 273
  26. 26.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 8 (b) 60 (c) 31 (d) 30
  27. 27.What is the missing term in the AP 1, 10, ?, 28, 37? (a) 28 (b) 20 (c) 18 (d) 19
  28. 28.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 6006 (c) 3003 (d) 2926
  29. 29.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2557 (c) 2485 (d) 5112
  30. 30.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  31. 31.What is the 23rd term of the AP 3, 6, 9, 12, …? (a) 66 (b) 72 (c) 70 (d) 69
  32. 32.Which term of the AP 1, 7, 13, 19, … is 121? (a) 21st (b) 20th (c) 23rd (d) 22nd
  33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  34. 34.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 13 (b) 12 (c) 11 (d) 16
  35. 35.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 122 (b) 26 (c) 238 (d) 119
  36. 36.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 267 (c) 528 (d) 264
  37. 37.Which term of the AP 10, 15, 20, 25, … is 60? (a) 13th (b) 12th (c) 11th (d) 10th
  38. 38.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 660 (b) 50 (c) 352 (d) 330
  39. 39.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 756 (d) 729
  40. 40.What is the 22nd term of the AP 11, 17, 23, 29, …? (a) 126 (b) 132 (c) 143 (d) 137

Answer key

  1. 3655
  2. 36
  3. 4186
  4. 330
  5. 21
  6. 98
  7. 103
  8. 121
  9. 30th
  10. 36
  11. 26
  12. 224
  13. 435
  14. 132
  15. 20
  16. 15
  17. 95
  18. 1431
  19. 190
  20. 37th
  21. 42
  22. 187
  23. 25
  24. 400
  25. 275
  26. 30
  27. 19
  28. 3003
  29. 2556
  30. 256
  31. 69
  32. 21st
  33. 144
  34. 12
  35. 119
  36. 264
  37. 11th
  38. 330
  39. 729
  40. 137

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