Question

Please help asap (:

What is the rule for the sequence with the first four terms below? 2.8, 2.2, 1.6, 1, ...

f(x)= 3.4 - 0.6x

f(x)=2.8 - 0.6x

f(x)= 3.4 (- 0.6) ^x

f(x)= 2.8 (0.6) ^x

Answer 1

f(1)=2.8, f(2)=2.2, f(3)=1.6, f(4)=1
f(2)-f(1)=2.2-2.8=-0.6
f(3)-f(2)=1.6-2.2=-0.6
f(4)-f(3)=1-1.6=-0.6
Then the function decreases 0.6 units by each unit increases x: Options 1 or 2

With the first function:
x=1→f(1)=3.4-0.6(1)=3.4-0.6→f(1)=2.8 OK

With the second function:
x=1→f(1)=2.8-0.6(1)=2.8-0.6→f(1)=2.2 NO

Answer: First option f(x)=3.4-0.6x

Answer 2

For this case we first define the variable:
x = number of terms.
The equation that models the problem is:
f (x) = 3.4 - 0.6x
We have then that the first four terms are:
x = 1
f (1) = 3.4 - 0.6 (1) = 3.4 - 0.6 = 2.8
x = 2
f (2) = 3.4 - 0.6 (2) = 3.4 - 1.2 = 2.2
x = 3
f (3) = 3.4 - 0.6 (3) = 3.4 - 1.8 = 1.6
x = 4
f (4) = 3.4 - 0.6 (4) = 3.4 - 2.4 = 1
Answer:
The rule for the sequence is:
f (x) = 3.4 - 0.6x
option 1