91Ó°ÊÓ

Find the function rule \(f(n)\) for each sequence. Then find the 20 th term in the sequence. $$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|}\hline n & 1 & 2 & 3 & 4 & 5 & 6 & \dots & n & \dots & 20 \\\\\hline f(n) & 3 & 9 & 15 & 21 & 27 & 33 & \dots & & \dots & \\\\\hline\end{array}$$

Into how many regions do 35 parallel lines in a plane divide that plane? (GRAPH CAN'T COPY).

\(\triangle D G T\) is isosceles with \(T D=D G .\) If the perimeter of \(D G T \quad\) is \(756 \mathrm{cm}\) and \(G T=240 \mathrm{cm},\) then \(D G=? .\) What type of reasoning do you use, inductive or deductive, when solving this problem?

use inductive reasoning to find the next two terms in each sequence. 7,3,-1,-5,-9,-13

use inductive reasoning to find the next two terms in each sequence. 1,3,6,10,15,21

The definition of a parallelogram says, "If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram" Quadrilateral LNDA has both pairs of opposite sides parallel. What conclusion can you make? What type of reasoning did you use?

If you draw 35 lines on a piece of paper so that no two lines are parallel to each other and no three lines are concurrent, how many times will they intersect? (GRAPH CAN'T COPY).

Write a deductive argument explaining why the Alternate Exterior Angles Conjecture is true. Assume that the Vertical Angles Conjecture and Corresponding Angles Conjecture are both true.

Find the appropriate geometric model, and solve. If 40 houses in a community all need direct lines to one another in order to have telephone service, how many lines are necessary? Is that practical? Sketch and describe two models: first, model the situation in which direct lines connect every house to every other house and, second, model a more practical alternative.

use inductive reasoning to find the next two terms in each sequence. 1,2,4,8,16,32