Question

What is a31 of the arithmetic sequence for which a5 = 12.4 and ag = : 22.4?

Answer 1

The value of a₃₁ of the arithmetic sequence exists 77.4.

How to find the value of a₃₁ of the arithmetic sequence?

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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