Answer
Total length cover after 10 swings = 130.26 inches
Work Step by Step
Pendulum covers length in first swing $a_{1}$ = 20 Inches
As next time pendulum swings 90% of previous swing means the swing length multiply by 0.9 each time, so common ratio = 0.9
Total length calculated for 10 swings then n = 10
Total length after n swings is given by sum formula $S_{n}$ = $a_{1}$$\frac{(1 - r^{n})}{(1 - r)}$
Total length cover after 10 swings $S_{10}$ = 20$\frac{(1 - 0.9^{10})}{(1 - 0.9)}$
= 20$\times$6.51 = 130.26 inches
