Question

I am not sure how to get the answer, please help!
A pendulum is set swinging. Its first oscillation is through an angle of 30 degrees, and each succeeding oscillation is through 95% of the angle of the one before it.
After how many swings is the angle through which it swings less than 1 degree?

Answer 1

this is a geometric series whose terms can be written
\( a, a r, a r^2, a r^3, \cdots \) where r is the common ratio

you have \(30, 30(0.95), 30(0.95)(0.95), \cdots \)

the nth term is given by \(t_n = ar^{n-1}\), so for example \(t_2 = ar^{2-1} \implies 30(0.95)\). [0.95 is your r for you.]

you want \(t_k = ar^{k-1} \lt 1 \)

Answer 2

Oh I had the common ratio wrong. I had 0.905. Ok, I am going to try again

Answer 3

I got the right thing now. Thank you very much for your help!