This is a geometric sequence with first term a1 = -4 and common ratio r = 4
so nth term = a1* r^(n-1)
= -4 *4^(n-1)
Answer:
Step-by-step explanation:
Each successive year, he
earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence(amount earned in the first year).
r represents the common ratio.
n represents the number of terms(years).
From the information given,
a = $32,000
r = 1 + 5/100 = 1.05
n = 20 years
The amount earned in his 20th year, T20 is
T20 = 32000 × 1.05^(20 - 1)
T20 = 32000 × 1.05^(19)
T20 = $80862.4
To determine the his total
earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as
Sn = (ar^n - 1)/(r - 1)
Therefore, the sum of the first 20 terms, S20 is
S20 = (32000 × 1.05^(20) - 1)/1.05 - 1
S20 = (32000 × 1.653)/0.05
S20 = $1057920
1) First find the multiplier.
Look at the 0 and 1st term you have 5 as the 0 and 3 as the 1st term.
2)Ask how do we get from 5 to 3?
- We subtract 2 so the multiplier is -2
3)Lets make a linear equation: y=mx +b
- m= multiplier or slope
- x= Just equals x value
- b= your starting value or the 0 term which is 5
4)Use the values that you have to create your equation.
Note:For the x value just plug in the x value from your table.
Ex.
Answer: 1.5 (D)
Explanation: I plotted the points on a graph and calculated the length of AC (20) and A’C’ (30)
The answer should be 30/20 = 1.5
I hope this helps!
So firstly, we have to find f(x) when x = 8 and x = 0. Plug the two numbers into the x variable of the function to solve for their f(x):
Now that we have their y's, we can use the slope, aka average rate of change, formula, which is . Using what we have, we can solve it as such:
In short, the average rate of change from x = 0 to x = 8 is 5/21.