MATHEMATIC 107
Sophia College Algebra
Unit 5 Milestone
17/22 that's 77%
Well done! If you keep getting Milestone scores like this you'll pass
the course.
17 questions were answered correctly.
5 questions were answered incorrectly.
1
RATIONALE
This is the formula to find the sum of a finite geometric sequence. We will use inform
given sequence to find values for , , and . Let's start by finding , the
first term.
In the above sequence, the first term is . So we will for in th
substitute geometric sequence formula. Next, let's determine the .
variable
To find , divide the value of any term by the value of the term before it to find th
, difference. For example, so . Finally, we need to review how many terms we
consider, which will be .
We are asked to find the sum of the first 10 terms, so . We can now substitute va
, , and to solve for .
Once the values for , , and have been plugged into the sum formula, we
the numerator.
to the power of is . Next, evaluate the subtraction in both the numerato
denominator.
minus is and minus is . Then, divide the numerator and d
The negative values in the numerator and denominator cancel to result in a positive
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
, RATIONALE
In the general exponential equation , the value will give us the location of th
Since , we know that the correct graph will have a y-intercept at . Next, we
can the end behavior of the graph by looking at the sign of .
Since is positive, we know that as tends towards positive infinity, also
positive infinity, and if tends towards negative infinity, tends towards zero.
Sophia College Algebra
Unit 5 Milestone
17/22 that's 77%
Well done! If you keep getting Milestone scores like this you'll pass
the course.
17 questions were answered correctly.
5 questions were answered incorrectly.
1
RATIONALE
This is the formula to find the sum of a finite geometric sequence. We will use inform
given sequence to find values for , , and . Let's start by finding , the
first term.
In the above sequence, the first term is . So we will for in th
substitute geometric sequence formula. Next, let's determine the .
variable
To find , divide the value of any term by the value of the term before it to find th
, difference. For example, so . Finally, we need to review how many terms we
consider, which will be .
We are asked to find the sum of the first 10 terms, so . We can now substitute va
, , and to solve for .
Once the values for , , and have been plugged into the sum formula, we
the numerator.
to the power of is . Next, evaluate the subtraction in both the numerato
denominator.
minus is and minus is . Then, divide the numerator and d
The negative values in the numerator and denominator cancel to result in a positive
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
, RATIONALE
In the general exponential equation , the value will give us the location of th
Since , we know that the correct graph will have a y-intercept at . Next, we
can the end behavior of the graph by looking at the sign of .
Since is positive, we know that as tends towards positive infinity, also
positive infinity, and if tends towards negative infinity, tends towards zero.
