An arithmetic sequence can be expressed as explicitly or recursively
The explicit formula of the sequence is [tex]a_n = 11 - 4n[/tex]
The recursive formula is given as:
[tex]a_n = a_{n -1} - 4[/tex]
[tex]a_1 = 7[/tex]
Substitute 2 for n in [tex]a_n = a_{n -1} - 4[/tex]
[tex]a_2 =a_1 - 4[/tex]
This gives
[tex]a_2 =7 - 4[/tex]
[tex]a_2 =3[/tex]
Calculate the common difference (d)
[tex]d = a_2 -a_1[/tex]
[tex]d = 3- 7[/tex]
[tex]d = -4[/tex]
The explicit formula is then calculated as:
[tex]a_n = a_1 + (n - 1)d[/tex]
This gives
[tex]a_n = 7+ (n - 1)*-4[/tex]
Expand
[tex]a_n = 7+4 - 4n[/tex]
[tex]a_n = 11 - 4n[/tex]
Hence, the explicit formula of the sequence is [tex]a_n = 11 - 4n[/tex]
Read more about arithmetic sequence at:
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