Answer
Fourth swing distance: $33.75$ cm
Total of first four swing distances: $218.75$ cm
Work Step by Step
Swing is 80 cm on first swing, successive swings are 3/4 of previous swing
Looking for fourth swing distance and sum of first four swing distances
$S_3 + $ 4th swing distance $=S_4$
$S_4 = (a_1)*(1-r^n)/(1-r)$
$a_1 = 80$
$r = .75$
$n=4$
$S_4 = (a_1)*(1-r^n)/(1-r)$
$S_4 = 80 *(1-.75^4)/(1-.75)$
$S_4 = 80*(1-.31640625)/.25$
$S_4 = 80*.68359375/.25$
$S_4= 80*2.734375$
$S_4 = 218.75$
$a_1 = 80$
$r = .75$
$n=3$
$S_3 = (a_1)*(1-r^n)/(1-r)$
$S_3 = 80*(1-.75^3)/(1-.75)$
$S_3 = 80 *(1-.421875)/.25$
$S_3=80*.578125/.25$
$S_3 = 80*2.3125$
$S_3 = 185$
$S_4 – S_3 =$ distance of fourth swing
$218.75-185$
$33.75$ cm is distance of fourth swing
