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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 881 · 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 33rd term of the AP 7, 12, 17, 22, …? (a) 160 (b) 167 (c) 165 (d) 172
  2. 2.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 180 (c) 13 (d) 90
  3. 3.What is the 14th term of the AP 6, 9, 12, 15, …? (a) 42 (b) 39 (c) 48 (d) 45
  4. 4.What is the 15th term of the AP 18, 21, 24, 27, …? (a) 63 (b) 45 (c) 60 (d) 42
  5. 5.What is the 13th term of the AP 17, 20, 23, 26, …? (a) 56 (b) 36 (c) 39 (d) 53
  6. 6.Which term of the AP 6, 14, 22, 30, … is 126? (a) 18th (b) 15th (c) 16th (d) 17th
  7. 7.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 22 (b) 31 (c) 24 (d) 23
  8. 8.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 17 (b) 84 (c) 154 (d) 77
  9. 9.What is the 19th term of the AP 18, 20, 22, 24, …? (a) 54 (b) 38 (c) 36 (d) 56
  10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  11. 11.Which term of the AP 14, 20, 26, 32, … is 134? (a) 20th (b) 22nd (c) 21st (d) 23rd
  12. 12.Which term of the AP 11, 14, 17, 20, … is 101? (a) 30th (b) 33rd (c) 32nd (d) 31st
  13. 13.What is the 31st term of the AP 15, 23, 31, 39, …? (a) 240 (b) 255 (c) 248 (d) 263
  14. 14.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 319 (b) 594 (c) 297 (d) 47
  15. 15.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 572 (b) 308 (c) 286 (d) 46
  16. 16.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 610 (b) 330 (c) 53 (d) 305
  17. 17.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 154 (b) 77 (c) 20 (d) 80
  18. 18.What is the 40th term of the AP 11, 19, 27, 35, …? (a) 323 (b) 331 (c) 312 (d) 320
  19. 19.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 18 (b) 20 (c) 19 (d) 23
  20. 20.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 190 (d) 361
  21. 21.Which term of the AP 8, 13, 18, 23, … is 153? (a) 29th (b) 31st (c) 32nd (d) 30th
  22. 22.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 222 (b) 240 (c) 35 (d) 444
  23. 23.What is the 37th term of the AP 8, 12, 16, 20, …? (a) 156 (b) 144 (c) 152 (d) 148
  24. 24.Which term of the AP 13, 20, 27, 34, … is 97? (a) 15th (b) 14th (c) 13th (d) 12th
  25. 25.What is the 26th term of the AP 8, 10, 12, 14, …? (a) 50 (b) 52 (c) 58 (d) 60
  26. 26.What is the 25th term of the AP 10, 13, 16, 19, …? (a) 72 (b) 85 (c) 82 (d) 75
  27. 27.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 324 (b) 47 (c) 600 (d) 300
  28. 28.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 58 (b) 110 (c) 55 (d) 17
  29. 29.What is the 36th term of the AP 1, 10, 19, 28, …? (a) 315 (b) 324 (c) 316 (d) 325
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  31. 31.Which term of the AP 11, 17, 23, 29, … is 227? (a) 37th (b) 38th (c) 36th (d) 39th
  32. 32.Which term of the AP 9, 18, 27, 36, … is 297? (a) 35th (b) 34th (c) 33rd (d) 32nd
  33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  34. 34.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 11 (b) 9 (c) 18 (d) 10
  35. 35.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 36 (c) 72 (d) 15
  36. 36.What is the sum of all the whole numbers from 1 to 41? (a) 1722 (b) 820 (c) 862 (d) 861
  37. 37.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 150 (b) 140 (c) 23 (d) 280
  38. 38.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 126 (b) 252 (c) 132 (d) 16
  39. 39.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 129 (b) 144 (c) 34 (d) 258
  40. 40.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 351 (c) 702 (d) 338

Answer key

  1. 167
  2. 90
  3. 45
  4. 60
  5. 53
  6. 16th
  7. 23
  8. 77
  9. 54
  10. 196
  11. 21st
  12. 31st
  13. 255
  14. 297
  15. 286
  16. 305
  17. 77
  18. 323
  19. 19
  20. 361
  21. 30th
  22. 222
  23. 152
  24. 13th
  25. 58
  26. 82
  27. 300
  28. 55
  29. 316
  30. 81
  31. 37th
  32. 33rd
  33. 625
  34. 10
  35. 64
  36. 861
  37. 140
  38. 126
  39. 129
  40. 351

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