Question 1
1 pts
Given the sequence:
25, 21, 17, 13,…
Write the explicit equation that models the sequence.
A. an
4n + 29
B. an
25 +(-4)(n-1)
C. an = -25 +(-4)(n-1)
D. an
= 4 + 25
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Question 1
1 pts
Given the sequence:
25, 21, 17, 13,…
Write the explicit equation that models the sequence.
A. an
4n + 29
B. an
25 +(-4)(n-1)
C. an = -25 +(-4)(n-1)
D. an
= 4 + 25
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Answer:
The correct answer is: Option B: [tex]a_n = 25+(-4)(n-1)[/tex]
Step-by-step explanation:
Given sequence is:
25, 21, 17, 13,…
Here
a1 = 25
a2 = 21
a3 = 17
First of all we have to determine the common difference. Common difference is the difference between consecutive terms of an arithmetic sequence.
So,
[tex]d = a_2 – a_1 = 21-25 = -4\\d =a_3-a_2 = 17-21 = -4[/tex]
The explicit formula is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
Putting the value of a1 and d
[tex]a_n = 25 + (n-1)(-4)\\a_n = 25-4n+4\\a_n = 29-4n[/tex]
Hence,
The correct answer is: Option B: [tex]a_n = 25+(-4)(n-1)[/tex]