Simplify the following expression using the distributive property.
2 answers:
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The complete question is:
A geometric sequence is defined recursively by
(a) Write out the first four terms of this sequence.
(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.
Answer:
- <u>The 9th term is larger than 1/10.</u>
Explanation:
You are given the first term, , and the recursive formula
Thus, you can find the sequence of terms by multiplying each term by the constant ratio, (-1/2).
<u>(a) First four terms of the sequence</u>
Those are the first four terms.
<u>(b) 9th term</u>
You can write the explicit formula of the sequence as:
Thus, for the 9th term, n = 9, and the term is:
Since 1/10 = 0.1, and 0.1 < 0.1526, the 9th term is larger than 1/10.
Answer:
∠ACG same side interior angles with ∠CGH and ∠CGE
Step-by-step explanation:
If parallel lines are drawn by a traverse certain angles (which have the same magnitude = equal) are created:
Corresponding Angles: same corners angles
Alternate Interior Angles: Alterative sides of the traverse, and the two crossed lines at the interior.
Alternate Exterior Angles: on the outer side of each of the two lines and on transversal opposite sides
Consecutive Interior Angles: To this side of the transverse with the two lines within. The Consecutive Inside Angles result in up to 180 ° when the two lines are parallel
As we can see from the figure
Alternate Interior Angles:
angles ∠ACG & ∠CGH and ∠DCG & ∠CGE
Consecutive Interior Angles:
angles ∠ACG & ∠CGE and ∠DCG & ∠CGH
Therefore ∠ACG same side interior angles with ∠CGH (Alternate Interior Angles) and ∠CGE (Consecutive Interior Angles)
