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Find the twenty-fourth term of the arithmetic sequence whose eighteenth term is 42, and whose twenty-fifth term is 56.
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Find the twenty-fourth term of the arithmetic sequence whose eighteenth term is 42, and whose twenty-fifth term is 56.

User Faiyaz
by
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1 Answer

10 votes

Answer:

54

Explanation:

Given

  • a₁₈ = 42
  • a₂₅ = 56

Solving

  • a₁₈ = a + 17d = 42 (1)
  • a₂₅ = a + 24d = 56 (2)
  • (2) - (1)
  • a + 24d - a - 17d = 56 - 42
  • 7d = 14
  • d = 2
  • a = 56 - 24(2) = 56 - 48
  • a = 8

Finding a₂₄

  • a₂₄ = a + 23d
  • 8 + 23(2)
  • 8 + 46
  • 54
User Jordi Kroon
by
2.6k points
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