the cost of renting a kayak for one hour is $23. Each additional hour is 8$ more. Write an explicit formula and recursive formul

Question

WARRIOR

1 month ago

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the cost of renting a kayak for one hour is $23. Each additional hour is 8$ more. Write an explicit formula and recursive formul

a to represent the situation.

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-02-28T18:40:31+03:00

Explicit formula $a_{n} =8n+15$

Recursive formula $\left \{ {{a_{1} =23} \atop {a_{n}=a_{n-1}+8 }} \right.$

To tackle this task, we will utilize an arithmetic sequence. The rental charge for one hour of a kayak is $23, and each subsequent hour costs an additional $8. Thus, the initial term of the sequence is 23, while each further hour adds 8, resulting in the sequence:

{23, 31, 39, 47, 55,.....,n}

We can formulate a recursive equation of the type $a_{n} =a_{n-1} +d$ , where $a_{n}$ signifies the nth term, n represents the number of terms, and d indicates the common difference within the sequence.

The common difference of the sequence {23, 31, 39, 47, 55,.....,n}. Consequently, the first term is $a_{1} =23$ , with the common difference being d = 8, reflecting the variation between each term.

$\left \{ {{a_{1} =23} \atop {a_{n} =a_{n-1}+8 }} \right.$

To express an explicit formula in the form $a_{n} =a_{1} +d(n-1)$ where $a_{n}$ indicates the nth term, n is the number of terms, $a_{1}$ denotes the first term of the sequence, and d signifies the common difference within the sequence.