The first swing of the pendulum travels 30cm. Each subsequent swing travels 90% as far as the previous swing. How long will it be on its 13th swing?

Answer 1

you have a geometric sequence

30, 27, 24.3, ...

a_n=a₁*r^(n-1) where a₁ is the first term, r=common ratio (90%=0.9), n=13th term

^a₁₃=30(0.9)^(13-1)

^a₁₃=30(0.9)¹²

a₁₃=30(0.2824295)

a₁₃=8.472885 (round as needed)