A new machine has just been installed to produce printed circuit boards. One of the critical measurements is the thickness of the resistance layer. The quality control inspector randomly selects five boards each half-hour, measures the thickness, and records the results. The measurements (in millimeters) for the period 8:00 a. m. to 10:30 a. m. follow. Thickness (millimeters)
Time 1 2 3 4 5
8:00 87.1 87.3 87.9 87.0 87.0
8:30 86.9 88.5 87.6 87.5 87.4
9:00 87.5 88.4 86.9 87.6 88.2
9:30 86.0 88.0 87.2 87.6 87.1
10:00 87.1 87.1 87.1 87.1 87.1
10:30 88.0 86.2 87.4 87.3 87.8

Mean of the sample means
= LCL = UCL =

Mean of the sample ranges
=LCL = UCL =

N=1,2,3,4,5 a n= 9,18,36,72,144 a recursive rule for the sequence is: f(1)= and f(n)= for n≥2. an explicit rule for the sequence is: f(n)= find a recursive rule and an explicit for the geometric sequence. 768,192,48,12,3,… a recursive rule for the sequence is: f(1)= and f(n)= for n≥2. an explicit rule for the sequence is: f(n)=∙ -1. concept 3: deriving the general forms of geometric sequence rules your turn use the geometric sequence to find a recursive rule and an explicit rule for any geometric sequence. 4,8,16,32,64,… recursive rule for the geometric sequence: f(1)= and f(n)=f(n-1)∙ for n≥2. recursive rule for any geometric sequence: given f(1),f(n)=f(n-1)∙ for n≥2. explicit rule for the geometric sequence: f(n)=∙-1. explicit rule for any geometric sequence: f(n)=∙-1 concept 4: constructing a geometric sequence given two terms your turn find an explicit rule for the sequence using subscript notation. the third term of a geometric sequence is 1/48 and the fifth term of the sequence is 1/432. all the terms of the sequence are positive. the explicit rule for the geometric sequence is