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Which function represents the arithmetic sequence shown in the graph.
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(C ) f (n)  27  3n .
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Given information: The graph is given below.
From the graph,
The first term of arithmetic sequence is 24.
The second term of arithmetic sequence is 21.
The third term of arithmetic sequence is 18.
The fourth term of arithmetic sequence is 15.
So the arithmetic sequence is {24,21,18,15}.
Calculation:
Formula :
An explicit formula for the nth term of an arithmetic sequence is given below.
an  a1  d (n  1) where a1 is the first term and d is the common difference.
So in the given arithmetic sequence a1 =24.
The common difference can be found by subtracting the first term from the second term.
d  a2  a1.
d  21  24.
d  3.
Substituting the common difference and first term of the arithmetic sequence into the
formula.
an  24  (3)( n  1).
an  24  3n  3.
an  27  3n.
So the nth term of the arithmetic sequence if represented by function f (n)  27  3n .
(C ) f (n)  27  3n .
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