Question 59350: Hello tutors could someone help with these word problems thanks Tine!
2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer:
Show work in this space.
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer:
Show work in this space.
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! 2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer: 3
Show work in this space.
To find the ratio, divide consecutive numbers, such as:
3/1=3
9/3=3
27=3, therefore the ratio = 3
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: 19683
Show work in this space.
Use the formula an=(a1)r^(n-1)
an=the nth term you are looking for
a1=the value of the first term
r=the ration
n=the number of the term you are looking for
So, to find the 10th term, plug-in the values:
a(10th term)=(1)(3)^(10-1)=19683
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer: 29,524
Sn=a1(1-r^n) /(1-r)
Sn=the sum of the first nth terms
a1=the value of the first term
r=the ratio
n=the number of the term
S(sum of the 10th term)=(1)((1-3^10) / (1-3)
S(10th)=29,524
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