Question

1).
Write the first four terms of a geometric sequence. Using the values you have written, calculate the common ratio and write the rule for the nth term. Show all calculations..
2)
You invest $500 in an account that has an annual interest rate of 8%, compounded weekly for 12 years. What is the equivalent interest rate and how many times will the money be compounded? How much will you have?

3)Suppose you make coffee and it starts off just too hot to drink, so you put it in the refrigerator temporarily to cool it off. If the original temperature is 190 degrees Fahrenheit and the refrigerator is 36 degrees Fahrenheit, what will the temperature of the coffee be after 3 minutes? (k = 0.12)

Answer 1

The formula for the nth term of ageometric sequence is given by An = ar^(n - 1), where a is the first term, n is the term number and r is the common ratio.

Write the first four terms of each geometric sequence?

a. a1=5 and r=2 

b. a1=6 and r=12

Algebra

1 Answer

Answer:

The first one: 5,10,20,40

The second one: 6,3,1.5,0.75

Explanation:

First, let's write the geometric sequences in an equation where we can plug them in:

an=a1⋅rn−1→a1 is the first term, r is the common ratio, n is the term you are trying to find (ex. the fourth term)

The first one is an=5⋅2n−1. The second one is an=6⋅(12)n−1.

First one:

We already know that the first term is 5. Let's plug in 2,3, and 4 to find the next three terms.

a2=5⋅22−1=5⋅21=5⋅2=10

a3=5⋅23−1=5⋅22=5⋅4=20

a4=5⋅24−1=5⋅2