A store pays $2 per pound for wood chips. One cubic foot of wood chips weighs about 15 pounds. What is the selling price of wood chips in the container shown if markup is 10%

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esmeraldavelez63

04.10.2020

Mathematics

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

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

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 $a_{n} =a_{n-1} +d$ where $a_{n}$ 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 $a_{1} =23$ , and the common diffenece is d = 8 which is the difference between each term.

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

Writing a explicit formula of the form $a_{n} =a_{1} +d(n-1)$ where where $a_{n}$ is the nth term, n the number of terms, $a_{1}$ the first term of the secuence, and d the common difference in the secuence.

With $a_{1}=23$ , and d = 8:

$a_{n} =23+8(n-1)$

$a_{n} =23+8n-8$

$a_{n} =8n+15$

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