3. Complete the table of values for this
sequence of matchstick
patterns.
1 2
3
4
5
Number of squares
Number of matchsticks
4
7
(i) How many matchsticks are required for the 6th pattern?
(ii) Find an expression in n for the number of matchsticks in the nth pattern.
(iii) Use the expression found to ascertain the number of matchsticks required for
the 50th pattern.
chotick

49/6 is going to equal 8 1/6

i believe b is the answer

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft