(score for question 3: of 4 points) 1. the sequence 6, 18, 54, 162, … shows the number of pushups kendall did each week, starting with her first week of exercising. (a) what is the recursive rule for the sequence? (b) what is the iterative rule for the sequence?

this is a geometric sequence with common ratio r

r = = = = 3

(a)

to obtain a term in the sequence multiply the previous term by 3

= 3 ← recursive rule

(b)

the n th term of a geometric sequence is

=

where is the first term and r the common ratio

= 6 × ← explicit rule

a net is a diagram that shows a “flattened” view of a solid. in a net, each face and base is shown with all of its dimensions. a net can also serve as a pattern to build a three-dimensional solid.

a pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.

" the net of a triangular pyramid consists of four triangles. the base here we are given of the pyramid is a equilateral   triangle, and the lateral faces are also triangles "