The first 3 figures in a pattern are shown.
Figure 1
Figure 2 Figure 3
= 1 small square
Which of the following functions represents f(n), the number of small squares in figure n?
A. f(n) = 2n2 + 1
OB. f(n) = (n + 1)2 - 1
OC. f(n) = (n + 1)2 + 1
o D. f(n) = n2 - 1

Answer:

a

Step-by-step explanation:

I dunno how to explain but A is the answer

The solution is, : A. f(n) = (n + 1)^2 – 1, the function represents f(n), the number of small squares in figure n.

Here, we have,

from the given diagram, we get,

the number of small squares in figures are,

Figure 1 is 3,

which be represented as,

3 = 4 - 1

 = 2² - 1

 = (1 + 1)² - 1

Figure 2 is 8  

which be represented as,

8 = 9 - 1

  = 3² - 1

  = (2 + 1)² - 1

Figure 3 is 15

which be represented as,

15 = 16 - 1

   = 4² - 1

   = (3 + 1)² - 1

so, we get,

the number of small squares in figure n will be,

The function is:

f(n) = (n + 1)² - 1

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