**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