Question

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

Answer 1

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