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Lesechka [4]
3 years ago
7

a sequence is defined by the explicit formula an = 3^n + 4. which recursive formula represents the same sequence of numbers?

Mathematics
1 answer:
Marta_Voda [28]3 years ago
5 0

Answer:

Recursive\ formula\ a_n=3a_{n-1}-8,\ a_1=7

Step-by-step explanation:

Recursive Formula: The formula that defines the every term of sequence using previous terms.

a_n=3^n+4\\\\a_1=3^1+4\\\\a_1=3+4\\\\a_1=7

a_n=3^n+4...................................(1)\\\\a_{n-1}=3^{n-1}+4..........................(2)\\\\Multiply\ by\ 3\ both\ the\ sides\\\\3a_{n-1}=3\times (3^{n-1}+4)\\\\3a_{n-1}=3\times 3^{n-1}+3\times 4\\\\3a_{n-1}=3^{n}+12\\\\3a_{n-1}==3^n+4+8\\\\From\ eq(1)\ 3^n+4=a_n\\\\3a_{n-1}=a_n+8\\\\Subtract\ 8\ from\ the\ both\ sides\\\\3a_{n-1}-8=a_n+8-8\\\\a_n=3a_{n-1}-8

Recursive\ formula\ a_n=3a_{n-1}-8,\ a_1=7

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Colt1911 [192]
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1) Focus:

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Which is now in the form a(x - h)^2 + k,
where:

a = 1/16 , h = - 8, and k = -6

(h,k) is the vertex: h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

=> a = 1/16 => p =1/4a = 16/4 = 4
 
y-componente of the focus = -6 + 4 = -2

x-component of the focus = h = - 8

=> focus = (-8, -2)

2) Vertex

We found it above, vertex = (h,k) = (-8,-6)


3) Directrix

It is the line y = p units below the vertex = > y = -6 - 4 = -10

y = -10   

 


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