Answer:
Arithmetic sequence
[tex]a_n=17-3n[/tex]
Step-by-step explanation:
We are given that a sequence
14,11,8,5,...
We have to identify sequence as arithmetic or geometric and write explicit formula for the sequence.
[tex]a_1=14[/tex]
[tex]a_2=11[/tex]
[tex]a_3=8[/tex]
[tex]d_1=a_2-a_1=11-14=-3[/tex]
[tex]d_2=a_3-a_2=8-11=-3[/tex]
[tex]d_3=a_4-a_3=5-8=-3[/tex]
[tex]d_1=d_2=d_3=-3[/tex]
When the difference of consecutive terms is constant then the sequence is arithmetic sequence.
Hence, the sequence is an arithmetic sequence.
[tex]a_n=a+(n-1)d[/tex]
substitute the values then we get
[tex]a_n=14+(n-1)(-3)=14-3n+3=17-3n[/tex]
Then, the explicit formula is given by
[tex]a_n=17-3n[/tex]
