Question

A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m. With each swing, she travels along an arc that is half as long as the arc of the previous swing. Which expression gives the total length the monkey swings in her first n swings?

Answer 1

L = 24 + 12 + 6 + 3 + 1.5 + 0.75 + 0.375 + 0.1875 + ......+ 0.5X(n-1)

Explanation:

Given:

Length travelled in first swing = 24m

In every swing the monkey travels half of the arc length

Total length of the first n swings = ?

Total length of n swings = length of first swing + 0.5 X length of first swing + .....+ length of n swings

L = 24 + 12 + 6 + 3 + 1.5 + 0.75 + 0.375 + 0.1875 + ......

Therefore, the expression that gives the total length of the monkey swings in her first n swings is

L = 24 + 12 + 6 + 3 + 1.5 + 0.75 + 0.375 + 0.1875 + ......+ 0.5X(n-1)

Answer 2

expression gives the total length the monkey swings in her first n swings is  $24(\frac{1}{2})^n$ .

Step-by-step explanation:

Here we have , A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m. With each swing, she travels along an arc that is half as long as the arc of the previous swing. We need to find Which expression gives the total length the monkey swings in her first n swings . Let's find out:

According to question ,  On the first swing, she passes through an arc whose length is 24 m and With each swing, she travels along an arc that is half as long as the arc of the previous swing .

For 1st swing :

⇒ $24(\frac{1}{2} )$

For 2nd swing :

⇒ $24(\frac{1}{2} )^2$

Hence  ,  expression gives the total length the monkey swings in her first n swings is

⇒ $24(\frac{1}{2})^n$

Therefore , expression gives the total length the monkey swings in her first n swings is  $24(\frac{1}{2})^n$ .