Recursive formula is: [tex]a_n = a_{n-1} -4[/tex]
Explicit formula is: [tex]a_n = 19-4n[/tex]
Step-by-step explanation:
Given sequence is:
15,11,7,3,-1
Here
[tex]a_1 = 15\\a_2 = 11\\a_3 = 7[/tex]
First of all, we have to find the common difference
Common difference is the difference between consecutive terms of an arithmetic sequence
So,
[tex]d = a_2-a_1 = 11-15 = -4\\d = a_3-a_2 = 7-11 = -4[/tex]
Recursive Formula:
A recursive formula is used to find the next term of an arithmetic sequence using previous term and common difference
General form of recursive formula for a given common difference d is:
[tex]a_n = a_{n-1} + d[/tex]
Putting the value of d
[tex]a_n = a_{n-1} -4[/tex]
Explicit Formula:
The explicit formula is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
Putting the first term and common difference
[tex]a_n = 15 + (n-1)(-4)\\a_n = 15 -4n+4\\a_n = 19-4n[/tex]
Hence,
Recursive formula is: [tex]a_n = a_{n-1} -4[/tex]
Explicit formula is: [tex]a_n = 19-4n[/tex]
Keywords: Arithmetic sequence, common difference
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