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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 959 · 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 7 terms of the AP 8, 13, 18, …? (a) 38 (b) 161 (c) 166 (d) 322
  2. 2.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 25 (b) 27 (c) 31 (d) 26
  3. 3.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 120 (c) 240 (d) 138
  4. 4.What is the 26th term of the AP 4, 13, 22, 31, …? (a) 238 (b) 225 (c) 229 (d) 234
  5. 5.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 1560 (c) 741 (d) 780
  6. 6.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 56 (b) 372 (c) 684 (d) 342
  7. 7.What is the 15th term of the AP 4, 13, 22, 31, …? (a) 135 (b) 126 (c) 130 (d) 139
  8. 8.What is the 23rd term of the AP 4, 10, 16, 22, …? (a) 138 (b) 136 (c) 142 (d) 132
  9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 72 (d) 64
  10. 10.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 190 (b) 28 (c) 200 (d) 380
  11. 11.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 631 (c) 630 (d) 595
  12. 12.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 85 (b) 25 (c) 95 (d) 170
  13. 13.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 25 (b) 26 (c) 7 (d) 50
  14. 14.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 55 (b) 60 (c) 110 (d) 21
  15. 15.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 145 (b) 28 (c) 290 (d) 160
  16. 16.What is the 38th term of the AP 17, 22, 27, 32, …? (a) 185 (b) 202 (c) 190 (d) 207
  17. 17.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 36 (b) 37 (c) 38 (d) 46
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 325 (d) 49
  20. 20.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 102 (b) 25 (c) 90 (d) 180
  21. 21.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  22. 22.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 272 (c) 120 (d) 128
  23. 23.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 130 (b) 65 (c) 17 (d) 70
  24. 24.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 26 (b) 20 (c) 21 (d) 19
  25. 25.Which term of the AP 7, 11, 15, 19, … is 163? (a) 42nd (b) 40th (c) 41st (d) 39th
  26. 26.What is the 25th term of the AP 8, 14, 20, 26, …? (a) 150 (b) 152 (c) 144 (d) 158
  27. 27.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  28. 28.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 28 (b) 56 (c) 29 (d) 7
  29. 29.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1326 (c) 1378 (d) 1352
  30. 30.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 870 (c) 436 (d) 435
  31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 841 (d) 870
  32. 32.What is the 21st term of the AP 11, 13, 15, 17, …? (a) 40 (b) 42 (c) 53 (d) 51
  33. 33.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 168 (b) 90 (c) 19 (d) 84
  34. 34.What is the 16th term of the AP 12, 14, 16, 18, …? (a) 30 (b) 42 (c) 44 (d) 32
  35. 35.What is the 14th term of the AP 2, 11, 20, 29, …? (a) 126 (b) 117 (c) 128 (d) 119
  36. 36.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 152 (b) 304 (c) 33 (d) 168
  37. 37.What is the 21st term of the AP 9, 15, 21, 27, …? (a) 120 (b) 126 (c) 135 (d) 129
  38. 38.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 600 (c) 276 (d) 288
  39. 39.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 11 (b) 13 (c) 20 (d) 12
  40. 40.What is the 12th term of the AP 16, 24, 32, 40, …? (a) 104 (b) 96 (c) 88 (d) 112

Answer key

  1. 161
  2. 26
  3. 120
  4. 229
  5. 780
  6. 342
  7. 130
  8. 136
  9. 64
  10. 190
  11. 630
  12. 85
  13. 25
  14. 55
  15. 145
  16. 202
  17. 37
  18. 81
  19. 625
  20. 90
  21. 361
  22. 136
  23. 65
  24. 20
  25. 40th
  26. 152
  27. 256
  28. 28
  29. 1378
  30. 435
  31. 841
  32. 51
  33. 84
  34. 42
  35. 119
  36. 152
  37. 129
  38. 300
  39. 12
  40. 104

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