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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 977 · 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 5 terms of the AP 9, 15, 21, …? (a) 210 (b) 33 (c) 105 (d) 120
  2. 2.Which term of the AP 3, 12, 21, 30, … is 138? (a) 18th (b) 16th (c) 17th (d) 15th
  3. 3.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 2701 (c) 2738 (d) 5550
  4. 4.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 370 (b) 340 (c) 61 (d) 680
  5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 196 (c) 210 (d) 27
  6. 6.Which term of the AP 3, 8, 13, 18, … is 178? (a) 35th (b) 36th (c) 38th (d) 37th
  7. 7.What is the 38th term of the AP 16, 21, 26, 31, …? (a) 190 (b) 206 (c) 185 (d) 201
  8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
  9. 9.What is the 17th term of the AP 15, 22, 29, 36, …? (a) 119 (b) 127 (c) 112 (d) 134
  10. 10.What is the 28th term of the AP 19, 23, 27, 31, …? (a) 127 (b) 108 (c) 131 (d) 112
  11. 11.What is the 30th term of the AP 16, 23, 30, 37, …? (a) 203 (b) 226 (c) 210 (d) 219
  12. 12.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 6320 (c) 3081 (d) 3161
  13. 13.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 324 (c) 42 (d) 612
  14. 14.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 43 (b) 506 (c) 275 (d) 253
  15. 15.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 105 (c) 91 (d) 98
  16. 16.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 32 (b) 33 (c) 39 (d) 34
  17. 17.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 22 (b) 130 (c) 140 (d) 260
  18. 18.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 704 (b) 352 (c) 385 (d) 62
  19. 19.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1770 (c) 3540 (d) 1711
  20. 20.What is the 15th term of the AP 13, 22, 31, 40, …? (a) 135 (b) 126 (c) 139 (d) 148
  21. 21.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  22. 22.Which term of the AP 15, 19, 23, 27, … is 63? (a) 14th (b) 12th (c) 13th (d) 15th
  23. 23.Which term of the AP 11, 14, 17, 20, … is 71? (a) 20th (b) 23rd (c) 21st (d) 22nd
  24. 24.Which term of the AP 18, 25, 32, 39, … is 151? (a) 22nd (b) 19th (c) 20th (d) 21st
  25. 25.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 85 (b) 100 (c) 170 (d) 29
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 36 (c) 15 (d) 72
  27. 27.What is the 11th term of the AP 9, 13, 17, 21, …? (a) 40 (b) 53 (c) 44 (d) 49
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 435 (d) 841
  29. 29.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 20 (b) 140 (c) 70 (d) 73
  30. 30.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 190 (b) 29 (c) 95 (d) 100
  31. 31.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 2862 (c) 1432 (d) 1431
  32. 32.What is the 34th term of the AP 9, 18, 27, 36, …? (a) 315 (b) 307 (c) 297 (d) 306
  33. 33.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 101 (b) 98 (c) 196 (d) 23
  34. 34.What is the 17th term of the AP 9, 15, 21, 27, …? (a) 96 (b) 111 (c) 102 (d) 105
  35. 35.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 8 (b) 31 (c) 30 (d) 60
  36. 36.What is the 23rd term of the AP 1, 8, 15, 22, …? (a) 161 (b) 154 (c) 155 (d) 162
  37. 37.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 10 (b) 12 (c) 11 (d) 13
  38. 38.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 78 (b) 138 (c) 19 (d) 69
  39. 39.What is the sum of all the whole numbers from 1 to 44? (a) 968 (b) 1980 (c) 990 (d) 946
  40. 40.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 120 (b) 66 (c) 15 (d) 60

Answer key

  1. 105
  2. 16th
  3. 2775
  4. 340
  5. 196
  6. 36th
  7. 201
  8. 324
  9. 127
  10. 127
  11. 219
  12. 3160
  13. 306
  14. 253
  15. 105
  16. 33
  17. 130
  18. 352
  19. 1770
  20. 139
  21. 676
  22. 13th
  23. 21st
  24. 20th
  25. 85
  26. 64
  27. 49
  28. 841
  29. 70
  30. 95
  31. 1431
  32. 306
  33. 98
  34. 105
  35. 30
  36. 155
  37. 11
  38. 69
  39. 990
  40. 60

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