he 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
The correct formulas that represent the same arithmetic sequence are:
1) lower a subscript 1 equals 5 and lower a subscript n equals lower a subscript n minus 1 plus 4
2) lower a subscript 1 equals 4 and lower a subscript n equals lower a subscript n minus 1 plus 5
The formula that represents the same arithmetic sequence is:
1. a₁ = 5, aₙ = aₙ₋₁ + 4 (option 1)
Explanation: In the original formula, the first term is 5 (a₁) and each subsequent term is obtained by adding 4 to the previous term (aₙ = aₙ₋₁ + 4).
To determine which of the formulas represents the same arithmetic sequence as the given function, we can compare the formulas to the given function.
The given function is: upper A left parenthesis n right parenthesis equals 5 plus left parenthesis n minus 1 right parenthesis left parenthesis 4 right parenthesis.
Let's examine each formula and see if they match the given function:
1. lower a subscript 1 equals 5
lower a subscript n equals lower a subscript n minus 1 plus 4
This formula matches the given function since it starts with 5 and each subsequent term is obtained by adding 4 to the previous term. Therefore, this formula represents the same arithmetic sequence.
2. lower a subscript 1 equals 4
lower a subscript n equals lower a subscript n minus 1 plus 5
This formula does not match the given function because it starts with 4 instead of 5. Therefore, this formula does not represent the same arithmetic sequence.
3. lower a subscript 1 equals 5
lower a subscript n equals lower a subscript n minus 1 minus 4
This formula does not match the given function because it subtracts 4 from the previous term instead of adding 4. Therefore, this formula does not represent the same arithmetic sequence.
4. lower a subscript n equals 4 minus 5 left parenthesis n minus 1 right parenthesis
This formula does not match the given function because it subtracts the term number multiplied by 5 instead of adding 4 to the previous term. Therefore, this formula does not represent the same arithmetic sequence.
5. lower a subscript n equals 4 plus 5 left parenthesis n minus 1 right parenthesis
This formula does not match the given function because it adds the term number multiplied by 5 instead of adding 4 to the previous term. Therefore, this formula does not represent the same arithmetic sequence.
So, the only formula that represents the same arithmetic sequence as the given function is:
lower a subscript 1 equals 5, and
lower a subscript n equals lower a subscript n minus 1 plus 4.