Question

Here is a growing pattern of sequences:

Answer 1

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