Answer:
a₅ = 40
Explanation:
The n th term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₇ = 25 and a₃ = 55 , then
a₁ + 2d = 55 → (1)
a₁ + 6d = 25 → (2)
Subtract (1) from (2) term by term to eliminate a₁, then
4d = - 30 ( divide both sides by 4 )
d = - 7.5
Substitute d = 7.5 into (1)
a₁ + 2(- 7.5) = 55
a₁ - 15 = 55 ( add 15 to both sides )
a₁ = 70
Thus
a₅ = 70 - 7.5(4) = 70 - 30 = 40