Answer:
A, C, F
Step-by-step explanation:
The first figure is drawn using 8 squares. The next uses 11 squares, and the one shown in Step 3 uses 14 squares. The numbers of blocks follow the sequence ...
8, 11, 14
which begins with 8 and increases by 3 from one step to the next. This constant increase from one term to the next makes it an arithmetic sequence.
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explicit form
The general term, an, of an arithmetic sequence can be written in terms of its first term, a1, and its common difference, d, as ...
an = a1 +d(n -1)
When the first term is a1=8, and the common difference is d=3, this becomes ...
an = 8 +3(n -1)
which simplifies to
an = 8 +3n -3 = 3n +5
Written in functional form, these explicit equations are ...
f(n) = 8 +3(n -1) . . . . . matches choice A
f(n) = 3n +5 . . . . . . . . matches choice F
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recursive form
The recursive form of the definition of a sequence starts with the first term, then tells you how to obtain the next term from that. Here, the first term is ...
f(1) = a1 = 8
and each term is 3 more than the last:
f(n) = 3 +f(n-1) . . . . . . . . . 3 is added to the previous term
Together, this is ...
f(n) = 8, f(n) = 3 +f(n -1) . . . . . matches choice C
