A. Arithmetic Sequence
B. The expression for given sequence is: a_n=3n
C. The 8th term is 24
Step-by-step explanation:
Given sequence is:
3,6,9,12……
A. Is this sequence arithmetic or geometric? How do you know that?
In order to dtermine if a given sequence is arithmetic or geometric, we find the common difference and common ratio
Common difference is the difference between consecutive terms of an arithmetic sequence
While common ratio is the ratio between two consecutive term of a geometric sequence
So,
Here
[tex]a_1=3\\a_2=6\\a_3=9\\d=a_2-a_1 = 6-3 =3\\d=a_3-a_2 = 9-6 = 3[/tex]
We can see that the common difference is same,
The given sequence is an arithmetic sequence
B. Find the expression that represents this sequence
The general form of arithmetic sequence is:
[tex]a_n=a_1+(n-1)d\\Putting\ the\ values\\a_n=3+(n-1)(3)\\a_n=3+3n-3\\a_n=3n[/tex]
The expression for given sequence is: a_n=3n
C. Find the 8th term of the sequence
The formula is:
a_n=3n
Putting n=8
[tex]a_8=3(8)\\a_8 = 24[/tex]
The 8th term of sequence is: 24
Keywords: Arithmetic sequence, Common difference
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