Answer:
The characteristic of an arithmetic sequence is:
- The difference between the consecutive terms is constant.
This difference between consecutive terms is called common difference and is denoted by (d)
STEP I
(finding the common difference)
As stated above, the common difference is the difference between consecutive terms and, thus, will be found out by subtracting any two consecutive terms.
-7 and -23 are two consecutive terms in the sequence!
Subtracting (-7) from (-23):
[tex] \implies \mathsf{d = - 23 - ( - 7)}[/tex]
[tex] \implies \mathsf{d = - 23 + 7}[/tex]
[tex] \implies \mathsf{ \underline{d = -16}}[/tex]
STEP II
(Finding the nth term)
The formula used for finding the nth term of an arithmetic sequence is:
[tex] \boxed{ \mathsf{a _{n} = a + (n - 1)d }}[/tex]
Here,
- [tex]a_n[/tex] = nth term
- a = first term
- d = common difference
The question asks us to find the 54th term of the sequence.
Substituting 54 for n:
[tex] \implies \mathsf{a _{54} = a + (54 - 1)d }[/tex]
- The first term of the sequence is -7
substituting -7 for a and -16 for d
[tex] \implies \mathsf{a _{54} = - 7+ (54 - 1)( - 16)}[/tex]
[tex] \implies \mathsf{a _{54} = - 7+ (53)( - 16)}[/tex]
[tex] \implies \mathsf{a _{54} = - 7 - 848}[/tex]
[tex] \implies \mathsf{ \underline{a _{54} = - 855}}[/tex]
ANSWER:
The 54th term of the sequence is -855.
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Learn more about nth term of an AP here:
https://brainly.com/question/16613594
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Hope this helps!
