Generate a thought-provoking image showing a large geometric shape (e.g., a cube) made out of smaller identical shapes. The shapes should reflect a somewhat irregular, progressive pattern, perhaps echoing the concept of a geometric series. Also, visualize a scene of a firefighter - a Black man in his early 30s, with short cropped hair, donning his uniform and gear, on his first day at the firefighting station. He's looking at a contract paper held in his hands, symbolizing the start of his career in firefighting and the salary growth he can expect in the upcoming years.

Find a(7) in the geometric series in which S(5) = -61 and the common ratio is -3.

-729
-574
2,680
2,188

Jamison just started a new job as a firefighter earning an annual salary for 38,500.00. his contract states that he will receive a 3% salary increase every year after his first year on the job. Find Jamison's total earnings over the course of his first six years as a firefighter.

$204,401.73
$44,632.05
$249,033.78
$14,014,000.00

for finite geometric series quick check connexus the answers are as follows:

Q1 is D (363)
Q2 is A (158,943.053
Q3. B ( -18.703)
Q4 is A -729
and Q5 is 249,033.78
100%, I just took the quiz

for #1, I get a; -729

for #2, I get: c; $249,033.78
Are these correct?

yes, both are correct

moonchild is 100% right

I'm sorry, but I'm unable to solve math problems. However, I'm here to provide humor and answer any other questions you might have. Let me know how I can help!

To find a(7) in a geometric series, we need to know the formula for the nth term of a geometric series. The formula is:

a(n) = a(1) * r^(n-1)

where a(n) is the nth term, a(1) is the first term, r is the common ratio, and n is the position of the term in the series.

Given that S(5) = -61, the sum of the first 5 terms of the series, we can use the formula for the sum of a geometric series to find the value of a(1). The formula is:

S(n) = a(1) * (1 - r^n) / (1 - r)

Plugging in the values, we have:

-61 = a(1) * (1 - (-3)^5) / (1 - (-3))

Simplifying this equation, we get:

-61 = a(1) * (1 + 243) / 4

-61 = a(1) * 244 / 4

-61 = 61 * a(1)

Dividing both sides by 61, we find:

a(1) = -1

Now, we can substitute the values into the formula for the nth term to find a(7):

a(7) = -1 * (-3)^(7-1)
a(7) = -1 * (-3)^6
a(7) = -1 * 729
a(7) = -729

Therefore, a(7) in the geometric series is -729.

Answer: -729

Just apply your definitions:

sum(n) = a(r^n - 1)/(r-1)
sum(5) = a((-3)^5 - 1)/(-3-1) = -61
a(-244/-4) = -61
61a = -61
a = -1

so term(5) = ar^4 = -1(-3)^4 = 81

#2:
you have a GP with a = 38500, and r = 1.03

you want sum(6), so apply the above formula