# 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

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?

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