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