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Score 21/22
You passed this Milestone
21 questions were answered correctly.
UNIT 5 — MILESTONE 5
1 question was answered incorrectly.
1
Find the sum of the first 10 terms of the following geometric sequences:
RATIONALE
This is the formula to find the sum of a finite geometric sequence. We will use
information from the given sequence to find values for a subscript 1, r, and n.
Let's start by finding a subscript 1, the value of the first term.
In the above sequence, the first term is . So we will substitute for
a subscript 1 in the sum of a geometric sequence formula. Next, let's determine the
variable r.
To find r, divide the value of any term by the value of the term before it to find the
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common difference. For example, so . Finally, we need to review how
many terms we want to consider, which will be n.
We are asked to find the sum of the first 10 terms, so n equals 10. We can now
substitute values in for a subscript 1, r, and n to solve for S subscript n.
Once the values for a subscript 1, r, and n have been plugged into the sum
formula, we can simplify the numerator.
2 to the power of 10 is 1024. Next, evaluate the subtraction in both the
numerator and denominator.
1 minus is and 1 minus is . Then, divide the numerator and
denominator.
The negative values in the numerator and denominator cancel to result in a positive
value of . Finally, multiply this by to find the sum.
The sum of the first ten terms in the sequence is .
CONCEPT
Sum of a Finite Geometric Sequence
2
Suppose we have two functions: and .
Find the value of .
RATIONALE
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To evaluate , evaluate and separately, and then multiply the
values together. Start by evaluating first by substituting for in the given
function.
is plugged in for all instances of in the function . Next, evaluate the
exponent.
squared is . Then, add and together.
plus is . Repeat this process for by substituting for in the given
function.
is plugged in for all instances of in the function . Next, evaluate the
multiplication.
times is . Then, add and together.
plus is . Finally multiply the results of and together.
We know that and . Multiply these values together.
times is .
CONCEPT
Multiplying and Dividing Functions
3
Evaluate the following expression using the properties of logarithms.
RATIONALE
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Score 21/22
You passed this Milestone
21 questions were answered correctly.
UNIT 5 — MILESTONE 5
1 question was answered incorrectly.
1
Find the sum of the first 10 terms of the following geometric sequences:
RATIONALE
This is the formula to find the sum of a finite geometric sequence. We will use
information from the given sequence to find values for a subscript 1, r, and n.
Let's start by finding a subscript 1, the value of the first term.
In the above sequence, the first term is . So we will substitute for
a subscript 1 in the sum of a geometric sequence formula. Next, let's determine the
variable r.
To find r, divide the value of any term by the value of the term before it to find the
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7789171 1/29
,2/5/2021 Sophia :: Welcome
common difference. For example, so . Finally, we need to review how
many terms we want to consider, which will be n.
We are asked to find the sum of the first 10 terms, so n equals 10. We can now
substitute values in for a subscript 1, r, and n to solve for S subscript n.
Once the values for a subscript 1, r, and n have been plugged into the sum
formula, we can simplify the numerator.
2 to the power of 10 is 1024. Next, evaluate the subtraction in both the
numerator and denominator.
1 minus is and 1 minus is . Then, divide the numerator and
denominator.
The negative values in the numerator and denominator cancel to result in a positive
value of . Finally, multiply this by to find the sum.
The sum of the first ten terms in the sequence is .
CONCEPT
Sum of a Finite Geometric Sequence
2
Suppose we have two functions: and .
Find the value of .
RATIONALE
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, 2/5/2021 Sophia :: Welcome
To evaluate , evaluate and separately, and then multiply the
values together. Start by evaluating first by substituting for in the given
function.
is plugged in for all instances of in the function . Next, evaluate the
exponent.
squared is . Then, add and together.
plus is . Repeat this process for by substituting for in the given
function.
is plugged in for all instances of in the function . Next, evaluate the
multiplication.
times is . Then, add and together.
plus is . Finally multiply the results of and together.
We know that and . Multiply these values together.
times is .
CONCEPT
Multiplying and Dividing Functions
3
Evaluate the following expression using the properties of logarithms.
RATIONALE
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