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Which recursive formula describes the patterns in the perimeter of the images?
A. an=an-1+2;a1=1
B. an=an-1+1;a1=1
C. an=an-1+2;a1=4
D. an=2an-1+1;a1=4

Which recursive formula describes the patterns in the perimeter of the images A anan12a11 B anan11a11 C anan12a14 D an2an11a14 class=

Respuesta :

apologiabiology
perimiters
adds 2 each time
starts with 4
so
an=4+2(n-1)



a1=4 so it is C or D

answer is C because it increases by 2 each time

Answer:

Option C is correct.

[tex]a_n =a_{n-1}+2[/tex]

[tex]a_1 =4[/tex]

Step-by-step explanation:

The arithmetic sequence says that:

For any sequence [tex]a_1, a_2, a_3, .....[/tex]

the recursive formula for this sequence is given by:

[tex]a_n =a_{n-1}+d[/tex]

where d represents the common difference of two consecutive terms and n is the number of terms.

Give the pattern in the figure:

for n = 1,   [tex]a_1 =4[/tex]

for n = 2,  [tex]a_2 =6[/tex]

for n = 3,   [tex]a_3 =8[/tex]

[tex]d =a_2-a_1 =6-4 = 2[/tex] or

[tex]d =a_3-a_2 =8-6= 2[/tex]

Now, substitute d =2 in the above formula we get;

[tex]a_n=a_{n-1}+2[/tex]

Therefore, recursive formula describes the patterns in the perimeter of the images is:

[tex]a_n=a_{n-1}+2[/tex]

[tex]a_1 = 4[/tex]