The first four terms of a sequence are shown below: 7,4,1,-2
which of the following functions best defines this sequence?
A) f(1)=7, f(n+1)= f(n)+3; for n>= 1
B) f(1)=7, f(n+1)= f(n)-3; for n >= 1
C) f(1)=7, f(n+1)= f(n)-4; for n >= 1
D) f(1)=7, f(n+1)= f(n)+4; for n >= 1

9514 1404 393

  B) f(1)=7, f(n+1)= f(n)-3; for n >= 1

Step-by-step explanation:

The first term of the sequence is 7 and the next (4) is found by adding -3 to that: 4 = 7-3. This is described in answer choice B.

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places