Answer to Question #145659 in Algebra for Bonevie tutor

Question

To solve problem involving arithmetic and geometric sequence and series.

A piece of paper is 0.05mm thick. For ten times, it is folded in half so that it's

thickness is doubled each time. How thick is the results?

Find the sum of all integers in between 100 and 1,000 that are exactly divisible by 7.

A ball is dropped 8m above the ground. On each rebound, the ball rises to one half

of the original height. (a) How high does it go on eight bounce? (b) How far has it

traveled, counting up and down distance only, it hits the floor for the ninth time?

Answer 1

1. a= T1= 0.05mm. T2 = 2T1. T3 = 2T2

r= T2/T1= 2

Sum = [a(rⁿ-1)]/ r-1 = [0.05(2¹⁰-1)] /( 2-1) = 51.15mm

2. a= T1= 105. l= 994. d = 7

l=a+(n-1)d

994 = 105 + (n-1)7

n-1 = 889/7 = 127

n= 1+127 = 128

S128 = n/2 (a+l) = 128/2 ( 105+ 994)

= 70336

3a T1= a = 8 r= 1/2

T8= ar⁷ = 8 × (0.5)⁷= 1/16

3b. S9 = [a(1-rⁿ)/ (1-r)] = [8(1-0.5⁹)/ (1-0.5)] = 15.9688m