Help with math (3 questions)

Question

1.Tell is True or false.The first term of a sequence with the recursive rule f(n)=2f(n-1)+2 is 4.
The second term is 6. T or F
The third term is 22. T or F
The fourth term is 46. T ir F

2.Ross earns 5% in commission each month. in the past 4 months he had each: $4000, $5200, $5500, $4900 Find a reasonable range for commission during these months.

3. Which explicit rule defines the sequence? -8,-6,-4
A. f(n)= -10-n
B.f(n)=-10+n^2
C.f(n)=n-9
D.f(n)=2n-10

Answer 1

Hi Jenny.  Hope this helps.

Q1:
First you need to determine what n is.

To do this - set up the function in terms of n.

 

f(n) = 2f(n-1)+2

f(1) = 4 (according to the problem statement)

f(2) = 2f(1) + 2 = 2(4) + 2 = 10

f(3) = 2f(2) + 2 = 2(10) + 2 = 22

f(4) = 2f(3) + 2 = 2(22) + 2 = 46

 

Q2:
If I understand the question correctly, it asks for a range of commissions earned over the past 4 months.

A range is defined as the area of variation between the upper and lower limits.

Therefore a range is between the lower limit and the upper limit.

 

Example:
Here is a set of ages:  5,12,6,18,24,45,32

The range of ages is 5-45 years of age.

 

Q3:

Let's test f(1) for each answer...

A.  f(1) = -10 - 1 = -11 (not -8)

B.  f(1) = -10 + 1² = -9 (not -8)

C.  f(1) = 1 - 9 = -8 (ah - ha!!!  A candidate!)

D.  f(1) = 2(1) - 10 = -8 (ah...another possible candidate)

 

So f(1) only works for C and D.

Try f(2) and f(3) to see which one is true for all values in the sequence.