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The value of a₃₁ of the arithmetic sequence exists 77.4.
<h3>How to find the value of a₃₁ of the arithmetic sequence?</h3>Given: a₅ = 12.4 and a₉ = : 22.4
For the arithmetic sequence a₁, a₂, a₃, ..., the n-th term exists
where d = common difference
a₅ = 12.4,
a₁ + 4d = 12.4 .........(1)
Because a₉ = 22.4,
a₁ + 8d = 22.4 .........(2)
Subtract (1) from (2), we get
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
Dividing throughout by 4, we get
d = 2.5
From (1), we get
a₁ = 12.4 - 4 2.5 = 2.4
a₃₁ = 2.4 + 30 2.5 = 77.4
Therefore, the correct answer is a₃₁ = 77.4
To learn more about the arithmetic sequence refer to; brainly.com/question/6561461
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