A ball on a pendulum moves 50 cm on its first swing. Each succeeding swing it moves 0.9 the distance of the previous swing

succeeding-swing
pendulum

#1

A ball on a pendulum moves 50 cm on its first swing. Each succeeding swing it moves 0.9 the distance of the previous swing. 1. Write the first 6 terms of the sequence generated. 2. Assuming the pattern continues, how far will the ball travel before coming to rest?

Answer:

This is again geometric based problems
and can be solved by using the formula
An = A1*{r^(n-1)} for finding particular term/s
where n = nth number of term
A1= first term ( 50cm)
r = common ratio which is 0.9 here.
for example 6th term will be
A6 = 50*{0.9^(5)}
= 50*0.59049
= 29.52 cm
simlarly, you can find any term.

and now since we have to find which is the last term(nearest to 0 bcz its neverending progression) when it come to rest.
by Hit and Try the last term Nearest to 0 (i.e. 0.009cm) comes to be the 83rd term
so sum upto the last term i.e. 83rd
Sn = A1*{1-r^n)}/((1-r)
= 50*{.99}?0.1
= 499.91 cm