# Ouestion

#### JST FRANKO

##### New member
A bob of a pendulum swings through an arc of 50cm on it first swing. Each successive swing is 90% of the length of the previous swing. Find the total distance the bob travels before comming to rest

#### Jomo

##### Elite Member
Yes, you are correct that this problem thought be under arithmetic.
What is preventing you from adding up all the terms? It is hard to help you if you fail to state where you are stuck. Please read the posting guidelines for this forum so that you know what you need to put into a post.

#### Dr.Peterson

##### Elite Member
A bob of a pendulum swings through an arc of 50cm on it first swing. Each successive swing is 90% of the length of the previous swing. Find the total distance the bob travels before comming to rest
Of course, theoretically infinite sums don't really belong in Arithmetic.

What have you learned about infinite series?

#### nasi112

##### Junior Member
$$\displaystyle 50 \ + \ 0.9 \cdot 50 \ + \ 0.9 \cdot 0.9 \cdot 50 \ + \ 0.9 \cdot 0.9 \cdot 0.9 \cdot 50 \ + \ ................. \ = \ ?$$

It seems that we have a geometric series here!