← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 237 · 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, 12, 16, …? (a) 140 (b) 154 (c) 32 (d) 280
  2. 2.What is the 16th term of the AP 2, 11, 20, 29, …? (a) 135 (b) 137 (c) 146 (d) 144
  3. 3.Which term of the AP 5, 12, 19, 26, … is 145? (a) 23rd (b) 21st (c) 22nd (d) 20th
  4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 42 (d) 11
  5. 5.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 5 (b) 6 (c) 7 (d) 4
  6. 6.What is the missing term in the AP 7, 14, ?, 28, 35? (a) 20 (b) 28 (c) 22 (d) 21
  7. 7.What is the 22nd term of the AP 6, 9, 12, 15, …? (a) 66 (b) 63 (c) 69 (d) 72
  8. 8.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3486 (c) 3570 (d) 7140
  9. 9.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 231 (d) 41
  10. 10.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 168 (b) 336 (c) 25 (d) 180
  11. 11.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 21 (b) 20 (c) 28 (d) 22
  12. 12.What is the 38th term of the AP 20, 26, 32, 38, …? (a) 242 (b) 222 (c) 248 (d) 228
  13. 13.Which term of the AP 6, 8, 10, 12, … is 60? (a) 27th (b) 30th (c) 29th (d) 28th
  14. 14.What is the 20th term of the AP 9, 17, 25, 33, …? (a) 169 (b) 160 (c) 152 (d) 161
  15. 15.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 55 (d) 406
  16. 16.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 256 (d) 31
  17. 17.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 20 (b) 11 (c) 12 (d) 13
  18. 18.What is the 13th term of the AP 14, 21, 28, 35, …? (a) 105 (b) 91 (c) 98 (d) 84
  19. 19.Which term of the AP 16, 24, 32, 40, … is 144? (a) 18th (b) 16th (c) 19th (d) 17th
  20. 20.What is the 16th term of the AP 1, 8, 15, 22, …? (a) 105 (b) 113 (c) 112 (d) 106
  21. 21.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 360 (b) 50 (c) 336 (d) 672
  22. 22.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 552 (d) 276
  23. 23.What is the 18th term of the AP 19, 21, 23, 25, …? (a) 55 (b) 34 (c) 36 (d) 53
  24. 24.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 240 (c) 121 (d) 120
  25. 25.What is the 13th term of the AP 20, 29, 38, 47, …? (a) 108 (b) 117 (c) 128 (d) 137
  26. 26.Which term of the AP 12, 15, 18, 21, … is 114? (a) 35th (b) 34th (c) 38th (d) 36th
  27. 27.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 30 (b) 40 (c) 32 (d) 31
  28. 28.Which term of the AP 10, 18, 26, 34, … is 154? (a) 18th (b) 19th (c) 21st (d) 20th
  29. 29.Which term of the AP 1, 7, 13, 19, … is 187? (a) 33rd (b) 32nd (c) 31st (d) 34th
  30. 30.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 72 (b) 84 (c) 144 (d) 22
  31. 31.What is the 19th term of the AP 13, 15, 17, 19, …? (a) 51 (b) 38 (c) 49 (d) 36
  32. 32.What is the missing term in the AP 18, ?, 30, 36, 42? (a) 25 (b) 23 (c) 24 (d) 30
  33. 33.What is the sum of all the whole numbers from 1 to 44? (a) 968 (b) 990 (c) 946 (d) 1980
  34. 34.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 7 (b) 13 (c) 8 (d) 9
  35. 35.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 13 (d) 28
  36. 36.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2592 (c) 5256 (d) 2628
  37. 37.Which term of the AP 3, 6, 9, 12, … is 99? (a) 33rd (b) 35th (c) 34th (d) 32nd
  38. 38.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 17 (b) 19 (c) 22 (d) 18
  39. 39.Which term of the AP 6, 10, 14, 18, … is 58? (a) 16th (b) 15th (c) 13th (d) 14th
  40. 40.Which term of the AP 16, 19, 22, 25, … is 46? (a) 13th (b) 11th (c) 12th (d) 10th

Answer key

  1. 140
  2. 137
  3. 21st
  4. 36
  5. 5
  6. 21
  7. 69
  8. 3570
  9. 441
  10. 168
  11. 21
  12. 242
  13. 28th
  14. 161
  15. 784
  16. 256
  17. 12
  18. 98
  19. 17th
  20. 106
  21. 336
  22. 529
  23. 53
  24. 120
  25. 128
  26. 35th
  27. 31
  28. 19th
  29. 32nd
  30. 72
  31. 49
  32. 24
  33. 990
  34. 8
  35. 49
  36. 2628
  37. 33rd
  38. 18
  39. 14th
  40. 11th

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad