Geometric/Arithmetic progression questions 2U (1 Viewer)

[kpad5991]

a) When light passes through one sheet of very thin glass, it's intensity is reduced by 3%. What is the minimum number of sheets that will reduce the intensity of the light below 1%?

b) find the formula for Tn for the GP 25, 5, 1 and solve the inequation Tn > 10^-6 using logarithms

 

[pikachu975]

a) Get a Tn formula and solve for Tn < 1

b) Use T2/T1 = T3/T2
5/25 = 1/5
So we know that r = 1/5

Therefore Tn = ar^(n-1)
Tn = 25*(1/5)^(n-1)

Tn > 10^-6
0.2^(n-1) > 10^-6 / 25
(n-1)*ln(0.2) > ln(10^-6 / 25)
n > [ ln(10^-6 / 25) / ln(0.2) ] + 1
n > 10.15

 

[braintic]

For (a), see my response to your same question in the Ext 2 thread.