Question

Kendyl is memorizing a piece of saxophone music to perform at a local festival. She currently has the first eight bars memorized and plans to memorize two more bars every day until she has the whole piece memorized. Write a recursive formula to model Kendyl’s progress.
(1 point)
Responses

a subscript n baseline equals 2 a subscript n minus 1 baseline semicolon a subscript 1 baseline equals 8
Image with alt text: a subscript n baseline equals 2 a subscript n minus 1 baseline semicolon a subscript 1 baseline equals 8

a subscript n baseline equals a subscript n minus 1 baseline plus 2 semicolon a subscript 1 baseline equals 6
Image with alt text: a subscript n baseline equals a subscript n minus 1 baseline plus 2 semicolon a subscript 1 baseline equals 6

a subscript n baseline equals 6 plus 2 n semicolon a subscript 1 baseline equals 8
Image with alt text: a subscript n baseline equals 6 plus 2 n semicolon a subscript 1 baseline equals 8

a subscript n baseline equals a subscript n minus 1 baseline plus 2 semicolon a subscript 1 baseline equals 8

Answer 1

To model Kendyl's progress in memorizing saxophone music using a recursive formula, we need to identify how her memorization changes each day.

Given that:
- She has 8 bars memorized initially.
- She memorizes 2 more bars every day.

We can define \(a_n\) as the total number of bars memorized on day \(n\).

1. **The base case**: On day 1, she has already memorized 8 bars, so \(a_1 = 8\).
2. **The recursive step**: Each subsequent day, she memorizes 2 additional bars, so the relationship can be defined as \(a_n = a_{n-1} + 2\).

Thus, the correct recursive formula is:
\[a_n = a_{n-1} + 2 \text{ for } n \geq 2\]
with the initial condition:
\[a_1 = 8\]

So, the correct response is:
**a subscript n baseline equals a subscript n minus 1 baseline plus 2 semicolon a subscript 1 baseline equals 8**.