Answer:
Step-by-step explanation:
Each term of this Geometric Series (3, −6, 12, −24, ...) can also be found through this explicit formula: Because the
term is found by the product of its common ratio "q", times its predecessor n-1. Where n, refers to the order of the term.
So let's test it, suppose we want to find the 4th term. We know the common ratio and the first term. Then we can write f(n) as:
f(4)=f(3)*-2⇒-24=12*-2⇒-24=-24
The explicit formula is ok.
Answers:
Reason 4: Isosceles triangle
Reason 5: Segment Addition Postulate
Reason 6: Segment Addition Postulate
Reason 7: Substitution
Reason 8: Substitution
Reason 9: Subtraction property of equality
Reason 10: Definition of congruence
Reason 11: Vertical Angles Theorem
Reason 12: Vertical Angles Theorem
Reason 13: ASA (angle side angle) congruence theorem
==================================
Explanations:
Reason 4: Triangle DCE is an isosceles triangle because of statement 1 of the proof table. The congruent base angles lead to congruent opposite sides.
Reason 5 and 6: This is the idea of breaking any segment into smaller pieces. The smaller pieces glue back together to get the larger original segment.
Reasons 7 and 8: Substitution is a math term which means "replacement". So for instance, in line 7 we started with DB = DC + CB (from line 6), then we replaced the "DB" with "DF" (see line 3); and then replaced "DF" with "DE+EF"
Reason 9: In this step, we subtract DE from both sides to have it go away and cancel out
Reason 10: If two lengths are equal, then the segments are congruent
Reason 11 & 12: Two angles are vertical if they are opposite from one another after forming from two lines crossing. Think of an X shape. Vertical angles are congruent.
Reason 13: We have two pairs of congruent angles, and a pair of congruent sides. The sides are between the angles. The order is important. See the attached image below.
