Sebastian writes the recursive formula f(x+1) = 4f(x) to
represent a geometric sequence whose second term is 12.
which explicit formula can be used to model the same?
sequence?
f(x) = 12(4)
f(x) = 3(4)x - 1
• f(x) = 4(12)*
f(x) = 4(3)* - 1

Step-by-step explanation leading to

Given: f(x+1) = 4*f(x)  [recursive] (1)  

and second term = 12

Need explicit formula  [non-recursive]

Solution:

A recursive formula is one which has the same term on both sides, but with different arguments, as in (1).

To visualize what (1) does, we set (arbitrarily) f(1)=1,  

so that using (1), we have

f(2) = 4*f(1) = 4

f(3) = 4*f(2) = 16

f(4) = 4*f(3) = 64,  

essentially we have a geometric series with common ratio of 4.

An explicit formula is f(x) = f(1)*(4^(x-1))   (2)

where the first term is interpreted as follows : f(1)=1.

We are given that the second term is 12, so we get

f(2) = f(1)*(4^(2-1), using equation (2)

substitute f(2) = 12 and Simplify:

12 = f(1)*(4^1) = 4*f(1) (3)

solve (3) for f(1)

f(1) = 12/4 = 3  (4)

x = 25

step-by-step explanation:

a^2+b^2=c^2

7^2+24^2=c^2

49+576=625

sqrt625=25

x=25

don't report but were is the digram

step-by-step explanation: