A sequence is called geometric if the ratio between successive terms is. 4 Skittles to the first customer, 7 to the second, 12 to the third, 19 to the fourth, etc. Many exercises in Addison-Wesley Geometry and Discrete Mathematics 12 will challenge your thinking. Opportunities for extensions of content, and for.

Jacquie Brodsky Mathematics Teacher Medway High School Thames V alley District School Board Robert Gleeson Mathematics Teacher Kincardine District Secondary School Bluewater District School Board Darren Luoma Mathematics Teacher Bear Creek Secondary School Simcoe County District School Board Marisa Palma Department Head of Mathematics St. Elizabeth Catholic High School Y ork Catholic District School Board C.

• Create a sequence of rectangles using this rule starting with a (1 times 2 ) rectangle. Then write out the sequence of perimeters for the rectangles (the first term of the sequence would be 6, since the perimeter of a (1 times 2 ) rectangle is 6 - the next term would be 10). • Repeat the above part this time starting with a (1 times 3 ) rectangle. • Find recursive formulas for each of the sequences of perimeters you found in parts (a) and (b). Don't forget to give the initial conditions as well. • Are the sequences arithmetic? If not, are they close to being either of these (i.e., are the differences or ratios almost constant)?

10 Consider the sequence (2, 7, 15, 26, 40, 57, ldots ) (with (a_0 = 2 )). By looking at the differences between terms, express the sequence as a sequence of partial sums. Then find a closed formula for the sequence by computing the (n )th partial sum.