Answer:
the recursive formula is an = an–1 + 2.9
Step-by-step explanation:
12.3+2.9=15.2
15.2+2.9=18.1
etc
The recursive formula of the given sequence is aₙ₊₁ = aₙ + 2.9.
An arithmetic sequence is defined as an arrangement of numbers which is a particular order.
The formula to find the general term of an arithmetic sequence is,
aₙ = a₁ + (n-1)d
In arithmetic, sequence d represents the common difference.
Where aₙ is the nth term of the sequence and a₁ is the first term
Recursive Formula for Arithmetic Sequence
The recursive formula to find the nth term of an arithmetic sequence is:
aₙ = aₙ₋₁ + d for n ≥ 2
where an is the nth term of an A.P.
Given the sequence 12.3, 15.2, 18.1, 21, 23.9, ...
The first term (a₁) = 12.3
a₂ = 15.2
a₃ = 18.1
a₄ = 21
a₅ = 23.9
The common difference (d) = a₅ - a₄= a₄ - a₃= a₃ - a₂ = 2.9
So, aₙ₊₁ - aₙ = 2.9
aₙ₊₁ = aₙ + 2.9
Hence, the recursive formula of the given sequence is aₙ₊₁ = aₙ + 2.9.
Learn more about arithmetic sequence here:
brainly.com/question/21961097
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