The function upper A left parenthesis n right parenthesis equals 5 plus left parenthesis n minus 1 right parenthesis left parenthesis 4 right parenthesis represents an arithmetic sequence. Which of the following formulas represents the same sequence? Select all that apply.
(1 point)
Responses
StartLayout Enlarged left-brace 1st Row lower a subscript 1 baseline equals 5 second row lower a subscript n baseline equals lower a subscript n minus 1 baseline plus 4 EndLayout
Image with alt text: StartLayout Enlarged left-brace 1st Row lower a subscript 1 baseline equals 5 second row lower a subscript n baseline equals lower a subscript n minus 1 baseline plus 4 EndLayout
StartLayout Enlarged left-brace 1st Row lower a subscript 1 baseline equals 4 second row lower a subscript n baseline equals lower a subscript n minus 1 baseline plus 5 EndLayout
Image with alt text: StartLayout Enlarged left-brace 1st Row lower a subscript 1 baseline equals 4 second row lower a subscript n baseline equals lower a subscript n minus 1 baseline plus 5 EndLayout
StartLayout Enlarged left-brace 1st Row lower a subscript 1 baseline equals 5 second row lower a subscript n baseline equals lower a subscript n minus 1 baseline minus 4 EndLayout
Image with alt text: StartLayout Enlarged left-brace 1st Row lower a subscript 1 baseline equals 5 second row lower a subscript n baseline equals lower a subscript n minus 1 baseline minus 4 EndLayout
lower a subscript n baseline equals 4 minus 5 left parenthesis n minus 1 right parenthesis
Image with alt text: lower a subscript n baseline equals 4 minus 5 left parenthesis n minus 1 right parenthesis
lower a subscript n baseline equals 4 plus 5 left parenthesis n minus 1 right parenthesis
Image with alt text: lower a subscript n baseline equals 4 plus 5 left parenthesis n minus 1 right parenthesis
lower a subscript n baseline equals 5 plus 4 left parenthesis n minus 1 right parenthesis
The following formulas represent the same arithmetic sequence as the given function:
1) a1 = 5, an = an-1 + 4
2) a1 = 4, an = an-1 + 5
5) an = 5 + 4(n-1)
To determine which formula represents the same arithmetic sequence as the given function, let's break down the given function and compare it to each formula:
Given function: upper A left parenthesis n right parenthesis equals 5 plus left parenthesis n minus 1 right parenthesis left parenthesis 4 right parenthesis
We can rewrite the function in a general arithmetic sequence form:
StartLayout Enlarged left-brace 1st Row upper a subscript 1 baseline equals 5 second row upper a subscript n baseline equals upper a subscript n minus 1 baseline plus 4 EndLayout
Now let's compare it with each formula:
Formula 1: StartLayout Enlarged left-brace 1st Row upper a subscript 1 baseline equals 5 second row upper a subscript n baseline equals upper a subscript n minus 1 baseline plus 4 EndLayout
This formula matches the given function and represents the same arithmetic sequence.
Formula 2: StartLayout Enlarged left-brace 1st Row upper a subscript 1 baseline equals 4 second row upper a subscript n baseline equals upper a subscript n minus 1 baseline plus 5 EndLayout
This formula doesn't match the given function, as the constant term is different.
Formula 3: StartLayout Enlarged left-brace 1st Row upper a subscript 1 baseline equals 5 second row upper a subscript n baseline equals upper a subscript n minus 1 baseline minus 4 EndLayout
This formula doesn't match the given function, as the arithmetic operation (minus) is different.
Formula 4: upper a subscript n baseline equals 4 minus 5 left parenthesis n minus 1 right parenthesis
This formula doesn't match the given function, as the constant term is different and the arithmetic operation (minus) is different.
Formula 5: upper a subscript n baseline equals 4 plus 5 left parenthesis n minus 1 right parenthesis
This formula doesn't match the given function, as the constant term is different.
Formula 6: upper a subscript n baseline equals 5 plus 4 left parenthesis n minus 1 right parenthesis
This formula doesn't match the given function, as the constant term is different.
Therefore, the formula that represents the same arithmetic sequence as the given function is:
Formula 1: StartLayout Enlarged left-brace 1st Row upper a subscript 1 baseline equals 5 second row upper a subscript n baseline equals upper a subscript n minus 1 baseline plus 4 EndLayout
The formula that represents the same arithmetic sequence as the function upper A left parenthesis n right parenthesis equals 5 plus left parenthesis n minus 1 right parenthesis left parenthesis 4 right parenthesis is:
1. lower a subscript 1 equals 5
lower a subscript n equals lower a subscript n minus 1 plus 4
Another formula that represents the same arithmetic sequence is:
2. lower a subscript 1 equals 4
lower a subscript n equals lower a subscript n minus 1 plus 5
So, the correct answers are options 1 and 2:
1. lower a subscript 1 equals 5
lower a subscript n equals lower a subscript n minus 1 plus 4
2. lower a subscript 1 equals 4
lower a subscript n equals lower a subscript n minus 1 plus 5