Answer:
-7
Step-by-step explanation:
We are given the following sequence:
[tex] \displaystyle \large{6,5,4,3,2,...}[/tex]
Checking if the sequence is arithmetic by using the following formula:
[tex] \displaystyle \large{a_{n + 1} - a_n = d}[/tex]
where d is a common difference. Common Difference means that these sequences must have same difference.
Let's check!
5-6 = -1
4-5 = -1
3-4 = -1
2-3 = -1
Since they are the same, the sequence is arithmetic.
General Term of Arithmetic Sequence
[tex] \displaystyle \large{a_n = a_1 + (n - 1)d}[/tex]
We know that a1 is 6 since 6 is the first term.
d is -1.
Our goal is to find a14. Therefore,
[tex] \displaystyle \large{a_{14} = 6 + (14 - 1)( - 1)} \\ \displaystyle \large{a_{14} = 6 + (13)( - 1)} \\ \displaystyle \large{a_{14} = 6 - 13} \\ \displaystyle \large{a_{14} = - 7}[/tex]
Therefore, the 14th term of sequence is -7.
