Question

Please help me with this one!

Answer 1

Answers:
Answer to part 1 is choice A) an = 15 + 8n
Answer to part 2 is choice D) a(n) = a(n-1)+8; a1 = 23

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Explanations:

For part 1, we use the general nth term formula for arithmetic sequences:
a(n) = a1 + d(n-1)

The first term is a1 = 23 and the common difference is d = 8
a(n) = a1 + d(n-1)
a(n) = 23 + 8(n-1)
a(n) = 23 + 8n - 8
a(n) = 15 + 8n
which is why the answer is choice A for part 1

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For the second part, we simply rephrase the given info into more mathematical notation. The first term is 23 so we simply write a1 = 23. The '1' is often written as a subscript so you can write it as $a_{1} = 23$

The recursive step is to add 8 to each term to get the next term. This is from the fact that each additional hour costs $8 extra. In math notation we write
a(n) = a(n-1) + 8
where a(n) and a(n-1) are the nth and (n-1)st terms respectively. This is function notation. We can write it as $a_{n} = a_{n-1}+8$ with the "n" and "n-1" as subscripts.

So that's why the answer is choice D for part 2