The explicit formula lower a subscript n baseline equals 2 minus 5 left parenthesis n minus 1 right parenthesis represents an arithmetic sequence. Write the recursive formula for the sequence.
(1 point)
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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 2 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 2 EndLayout
StartLayout Enlarged left-brace 1st Row lower a subscript 1 baseline equals 2 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 2 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 2 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 2 EndLayout
StartLayout Enlarged left-brace 1st Row lower a subscript 1 baseline equals 2 second row lower a subscript n baseline equals lower a subscript n minus 1 baseline minus 5 EndLayout
The recursive formula for the arithmetic sequence is:
\[a_1 = 2\]
\[a_n = a_{n-1} - 5\]
The correct recursive formula for the arithmetic sequence represented by the explicit formula "lower a subscript n baseline equals 2 minus 5 left parenthesis n minus 1 right parenthesis" is:
lower a subscript 1 baseline equals 2
lower a subscript n baseline equals lower a subscript n minus 1 baseline plus 5
The recursive formula for an arithmetic sequence is a formula that defines each term in the sequence based on the previous term.
In this case, the explicit formula given is:
a_n = 2 - 5(n - 1)
To find the recursive formula, we need to express a_n in terms of a_n-1.
Notice that a_n-1 is the previous term in the sequence, so we can substitute n-1 for n in the explicit formula to find a_n-1:
a_n-1 = 2 - 5((n-1) - 1)
Now, to find the recursive formula, we want to express a_n in terms of a_n-1:
a_n = a_n-1 + d
Where d is the common difference in the sequence. In this case, the common difference is -5.
Substituting the values we found:
a_n = (2 - 5((n-1) - 1)) - 5
Simplifying further:
a_n = 2 - 5n + 5 - 5
a_n = -5n + 2
Therefore, the recursive formula for this arithmetic sequence is:
a_1 = 2
a_n = a_n-1 - 5