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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 253 · 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 8, 10, 12, …? (a) 60 (b) 65 (c) 16 (d) 120
  2. 2.Which term of the AP 17, 24, 31, 38, … is 157? (a) 20th (b) 23rd (c) 22nd (d) 21st
  3. 3.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 210 (d) 39
  4. 4.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 8 (b) 9 (c) 6 (d) 7
  5. 5.What is the 24th term of the AP 12, 20, 28, 36, …? (a) 204 (b) 192 (c) 196 (d) 184
  6. 6.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 8742 (c) 4278 (d) 4372
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 64 (d) 36
  8. 8.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 14 (b) 61 (c) 60 (d) 120
  9. 9.What is the missing term in the AP 15, ?, 25, 30, 35? (a) 25 (b) 19 (c) 21 (d) 20
  10. 10.What is the 13th term of the AP 19, 22, 25, 28, …? (a) 58 (b) 55 (c) 36 (d) 39
  11. 11.Which term of the AP 5, 14, 23, 32, … is 230? (a) 28th (b) 25th (c) 26th (d) 27th
  12. 12.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 29 (b) 126 (c) 228 (d) 114
  13. 13.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 26 (c) 50 (d) 25
  14. 14.Which term of the AP 20, 25, 30, 35, … is 210? (a) 39th (b) 38th (c) 42nd (d) 40th
  15. 15.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4656 (c) 4754 (d) 4753
  16. 16.Which term of the AP 7, 13, 19, 25, … is 121? (a) 19th (b) 22nd (c) 20th (d) 21st
  17. 17.What is the 39th term of the AP 19, 24, 29, 34, …? (a) 214 (b) 209 (c) 195 (d) 190
  18. 18.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 90 (b) 48 (c) 45 (d) 15
  19. 19.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4951 (c) 9900 (d) 4851
  20. 20.What is the 30th term of the AP 8, 11, 14, 17, …? (a) 90 (b) 98 (c) 95 (d) 87
  21. 21.What is the 18th term of the AP 2, 7, 12, 17, …? (a) 92 (b) 87 (c) 90 (d) 85
  22. 22.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 212 (b) 209 (c) 34 (d) 418
  23. 23.What is the 30th term of the AP 10, 16, 22, 28, …? (a) 190 (b) 174 (c) 184 (d) 180
  24. 24.What is the 15th term of the AP 4, 10, 16, 22, …? (a) 84 (b) 94 (c) 90 (d) 88
  25. 25.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 26 (b) 23 (c) 22 (d) 21
  26. 26.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 7656 (c) 3829 (d) 3741
  27. 27.What is the 10th term of the AP 5, 13, 21, 29, …? (a) 72 (b) 80 (c) 77 (d) 85
  28. 28.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2628 (c) 2556 (d) 2592
  29. 29.What is the 40th term of the AP 10, 13, 16, 19, …? (a) 117 (b) 120 (c) 127 (d) 130
  30. 30.What is the 28th term of the AP 12, 16, 20, 24, …? (a) 120 (b) 112 (c) 124 (d) 108
  31. 31.Which term of the AP 15, 22, 29, 36, … is 253? (a) 35th (b) 34th (c) 37th (d) 36th
  32. 32.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 29 (b) 418 (c) 220 (d) 209
  33. 33.What is the 24th term of the AP 17, 20, 23, 26, …? (a) 69 (b) 72 (c) 89 (d) 86
  34. 34.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 21 (d) 36
  35. 35.What is the 39th term of the AP 20, 24, 28, 32, …? (a) 172 (b) 156 (c) 152 (d) 176
  36. 36.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 324 (b) 47 (c) 300 (d) 600
  37. 37.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 900 (d) 930
  38. 38.What is the 35th term of the AP 5, 9, 13, 17, …? (a) 145 (b) 136 (c) 140 (d) 141
  39. 39.What is the 16th term of the AP 6, 8, 10, 12, …? (a) 38 (b) 36 (c) 30 (d) 32
  40. 40.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 390 (b) 780 (c) 60 (d) 420

Answer key

  1. 60
  2. 21st
  3. 400
  4. 7
  5. 196
  6. 4371
  7. 64
  8. 60
  9. 20
  10. 55
  11. 26th
  12. 114
  13. 25
  14. 39th
  15. 4753
  16. 20th
  17. 209
  18. 45
  19. 4950
  20. 95
  21. 87
  22. 209
  23. 184
  24. 88
  25. 22
  26. 3828
  27. 77
  28. 2628
  29. 127
  30. 120
  31. 35th
  32. 209
  33. 86
  34. 36
  35. 172
  36. 300
  37. 900
  38. 141
  39. 36
  40. 390

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