Maureen is painting horizontal stripes on a wall for a mural

Maureen is painting horizontal stripes on a wall for a mural. The first stripe is certain number of centimeters, c. The second stripe is 3/4 the length of the first stripe, and each subsequent stripe is 3/4 the length of the previous stripe. For example , the second stripe is 3/4c. Which of the following represents the total number of centimeters that Maureen will paint if she paints 9 stripes? Explain Answer.

Solution

First stripe = c cm

2nd strip = 3c/4 cm

3rd strip = 3/4(3c/4) = (3/4)^2c

4rth strip = 3/4(9c/16) = c(3/4)^3

and so on..

G.P. series = c +3c/4 +9c/16 + 27c/64 .... = c[ 1+ 3/4 +9/16 +27/64 .......]

there are 9 9 terms in series

Sum of G.P = a(1 - r^n)/(1-r) = c{ 1(1 -(3/4)^9/( 1-3/4) }

= c(242461/4^9*1/4)

= c( 242461/4^8)

= 3.699c cm ( Total cm\'s he painted)