Answer:
The next terms of the sequence 33, 25, 17 is:
[tex]a_4=9[/tex]
[tex]a_5=1[/tex]
Step-by-step explanation:
[tex]3, 25, 17...[/tex]
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
[tex]25-33=-8,\:\quad \:17-25=-8[/tex]
The difference between all the adjacent terms is the same and equal to
[tex]d=-8[/tex]
The first element of the sequence is:
[tex]a_1=33[/tex]
now substituting [tex]a_1=33[/tex] and [tex]d=-8[/tex] in the nth term
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=-8\left(n-1\right)+33[/tex]
[tex]a_n=-8n+41[/tex]
Determining the 4th term:
We already got the nth term of the Arithmetic sequence
[tex]a_n=-8n+41[/tex]
substitute n = 4
[tex]a_4=-8\left(4\right)+41[/tex]
[tex]a_4=-32+41[/tex]
[tex]a_4=9[/tex]
Determining the 5th term:
substitute n = 5 in the nth term
[tex]a_n=-8n+41[/tex]
[tex]a_5=-8\left(5\right)+41[/tex]
[tex]a_5=-40+41[/tex]
[tex]a_5=1[/tex]
Thus, the next terms of the sequence 33, 25, 17 is:
[tex]a_4=9[/tex]
[tex]a_5=1[/tex]
