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Here is a growing pattern of sequences:

Here is a growing pattern of sequences:-example-1
User Ujjwal
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1 Answer

15 votes
15 votes

Answer:

A, C, F

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

User Xbello
by
3.2k points
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