Explicit formula [tex]a_{n} =8n+15[/tex]
Recursive formula [tex]\left \{ {{a_{1} =23} \atop {a_{n}=a_{n-1}+8 }} \right.[/tex]
To solve this problem we have to use an arithmetic sequence. The cost of renting a kayak for 1 hour is $23, each additional hour is $8 more. So, the first element of the secuence will be 23 for one hour, then each addittional hour will be 23 + 8, making the secuence:
{23, 31, 39, 47, 55,.....,n}
Writing a recursive formula of the form [tex]a_{n} =a_{n-1} +d[/tex] where [tex]a_{n}[/tex] is the nth term, n the number of terms, and d the common difference in the secuence.
The common difference of the secuence {23, 31, 39, 47, 55,.....,n}. So, the first term is [tex]a_{1} =23[/tex], and the common diffenece is d = 8 which is the difference between each term.
[tex]\left \{ {{a_{1} =23} \atop {a_{n} =a_{n-1}+8 }} \right.[/tex]
Writing a explicit formula of the form [tex]a_{n} =a_{1} +d(n-1)[/tex] where where [tex]a_{n}[/tex] is the nth term, n the number of terms, [tex]a_{1}[/tex] the first term of the secuence, and d the common difference in the secuence.
With [tex]a_{1}=23[/tex], and d = 8:
[tex]a_{n} =23+8(n-1)[/tex]
[tex]a_{n} =23+8n-8[/tex]
[tex]a_{n} =8n+15[/tex]
