Given:
A tree is currently 10 feet tall and grows 2 feet per year.
To find:
The arithmetic sequence in explicit formula that can model this scenario.
Solution:
Current height of tree is 10 feet. So, initial value of the arithmetic sequence is a=10.
It grows 2 feet per year. So, common difference is d=2.
The explicit formula for an arithmetic sequence is
[tex]f(n)=a+(n-1)d[/tex]
where, a is first term and d is common difference.
Put a=10 and d=2 in the above formula.
[tex]f(n)=10+(n-1)2[/tex]
[tex]f(n)=10+2n-2[/tex]
[tex]f(n)=8+2n[/tex]
Therefore, the explicit formula for given scenario is [tex]f(n)=8+2n[/tex].
