1. ## Geometric progression problem.

Diagram shows the first four squares from a series of squares.The side of these squares decreases in a geometric progression.The side of the first square is $\displaystyle h$ cm and the side of the subsequent square is $\displaystyle \frac{3}{4} h$. cm

a)if the sum of the perimeters of the first five squares is $\displaystyle \frac{781}{4}cm$. find the value of $\displaystyle h$.

b)Hence,find the area of the $\displaystyle 5^{th}$ square.

2. (a)

The perimeter of the 1st square is $\displaystyle 4h$.

The perimeter of the 2nd square is $\displaystyle 4\left(\frac{3}{4}h\right)$

The perimeter of the 3rd square is $\displaystyle 4\left(\frac{3}{4}\left[\frac{3}{4}h\right]\right)$

Continue in that way and sum the perimeters of the first five squares to find $\displaystyle h$