By using arithmetic sequence, the equation explicit formula for the situation is [tex]a_{n}=1.5n-15.5[/tex]
([tex]n\geq 1[/tex] and n is a whole number).
What is an arithmetic sequence?
"Arithmetic sequences (arithmetic progressions) are ordered set of numbers that have a common difference between each consecutive term.
If we add or subtract the same number each time to make the sequence, it is an arithmetic sequence."
Given
It is an arithmetic sequence
[tex]a_{2}[/tex] = 18.5, [tex]a_{n}= a_{n-1}+1.5[/tex]
so, [tex]a_{1}= a_{2}-1.5[/tex]
⇒[tex]a_{1}= 18.5-1.5[/tex]
⇒[tex]a_{1}= 17[/tex]
Common difference d = 1.5
Formula to find the equivalent explicit formula
[tex]a_{n}=a_{1}+(n-1)d[/tex]
⇒[tex]a_{n}=17+(n-1)1.5[/tex]
⇒[tex]a_{n}=17+1.5n-1.5[/tex]
⇒[tex]a_{n}=1.5n-15.5[/tex]
Hence, The equation explicit formula for the situation is [tex]a_{n}=1.5n-15.5[/tex]
([tex]n\geq 1[/tex] and n is a whole number).
Learn more about arithmetic sequence here
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