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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 695 · 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 20th term of the AP 16, 25, 34, 43, …? (a) 171 (b) 187 (c) 196 (d) 180
  2. 2.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 132 (b) 242 (c) 121 (d) 21
  3. 3.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 1892 (c) 903 (d) 946
  4. 4.What is the 11th term of the AP 9, 12, 15, 18, …? (a) 33 (b) 39 (c) 30 (d) 42
  5. 5.What is the 29th term of the AP 17, 19, 21, 23, …? (a) 58 (b) 73 (c) 75 (d) 56
  6. 6.What is the 16th term of the AP 18, 23, 28, 33, …? (a) 75 (b) 98 (c) 93 (d) 80
  7. 7.What is the 10th term of the AP 2, 10, 18, 26, …? (a) 74 (b) 80 (c) 82 (d) 72
  8. 8.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 46 (b) 286 (c) 572 (d) 308
  9. 9.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2556 (c) 2557 (d) 2485
  10. 10.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 170 (b) 90 (c) 85 (d) 27
  11. 11.Which term of the AP 12, 16, 20, 24, … is 140? (a) 34th (b) 33rd (c) 35th (d) 32nd
  12. 12.What is the 39th term of the AP 8, 15, 22, 29, …? (a) 274 (b) 266 (c) 273 (d) 281
  13. 13.Which term of the AP 5, 12, 19, 26, … is 96? (a) 13th (b) 14th (c) 16th (d) 15th
  14. 14.What is the 16th term of the AP 19, 24, 29, 34, …? (a) 75 (b) 99 (c) 80 (d) 94
  15. 15.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 1326 (c) 1352 (d) 2756
  16. 16.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 192 (b) 372 (c) 21 (d) 186
  17. 17.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 225 (c) 243 (d) 450
  18. 18.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 19 (b) 21 (c) 17 (d) 18
  19. 19.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 8 (b) 7 (c) 9 (d) 6
  20. 20.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 12 (b) 11 (c) 13 (d) 15
  21. 21.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 2970 (c) 1458 (d) 1485
  22. 22.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  23. 23.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 4290 (c) 2145 (d) 2080
  24. 24.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 342 (c) 171 (d) 153
  25. 25.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1891 (c) 1953 (d) 3906
  26. 26.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 2416 (c) 4830 (d) 2415
  27. 27.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 26 (b) 23 (c) 24 (d) 25
  28. 28.Which term of the AP 6, 11, 16, 21, … is 46? (a) 10th (b) 11th (c) 8th (d) 9th
  29. 29.What is the 27th term of the AP 18, 23, 28, 33, …? (a) 148 (b) 130 (c) 153 (d) 135
  30. 30.What is the 13th term of the AP 7, 10, 13, 16, …? (a) 39 (b) 36 (c) 43 (d) 46
  31. 31.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 25 (b) 26 (c) 7 (d) 50
  32. 32.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 25 (b) 320 (c) 160 (d) 170
  33. 33.What is the 30th term of the AP 2, 4, 6, 8, …? (a) 58 (b) 60 (c) 62 (d) 61
  34. 34.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 99 (b) 180 (c) 90 (d) 18
  35. 35.What is the 37th term of the AP 3, 11, 19, 27, …? (a) 291 (b) 296 (c) 299 (d) 288
  36. 36.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 29 (d) 225
  37. 37.What is the 25th term of the AP 6, 14, 22, 30, …? (a) 200 (b) 198 (c) 206 (d) 192
  38. 38.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 480 (b) 900 (c) 65 (d) 450
  39. 39.What is the 15th term of the AP 17, 23, 29, 35, …? (a) 107 (b) 101 (c) 84 (d) 90
  40. 40.Which term of the AP 17, 19, 21, 23, … is 31? (a) 7th (b) 10th (c) 9th (d) 8th

Answer key

  1. 187
  2. 121
  3. 946
  4. 39
  5. 73
  6. 93
  7. 74
  8. 286
  9. 2556
  10. 85
  11. 33rd
  12. 274
  13. 14th
  14. 94
  15. 1378
  16. 186
  17. 225
  18. 18
  19. 7
  20. 12
  21. 1485
  22. 900
  23. 2145
  24. 171
  25. 1953
  26. 2415
  27. 24
  28. 9th
  29. 148
  30. 43
  31. 25
  32. 160
  33. 60
  34. 90
  35. 291
  36. 225
  37. 198
  38. 450
  39. 101
  40. 8th

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