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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

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  • 10 de febrero de 2023
  • 28
  • 2022/2023
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  • mathematic 107 sophia college algebra unit 5 milestone 1722 thats 77 well done if you keep getting milestone scores like this youll pass the course 17 questions were answered correctly 5

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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.

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