The total distance the monkey has traveled when she completes her 25th swing is 92.82 m if the monkey is swinging from a tree.
What is a sequence?
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
A monkey is swinging from a tree. On the first swing, she passes through an arc of 10 m. With each swing, she passes through an arc 9/10 the length of the previous swing.
In first swing = 10 m
In second swing = (9/10)10 m = 9 m
In the second swing = (9/10)9 =81/10
10, 9, 81/10,..
This is the geometric sequence with the first term being 10 and the common ratio being 9/10.
a = 10
r = 9/10
The sum of geometric sequence up to 25th terms:
S = a(1 - rⁿ)/(1 - r)
S = 10(1 - (9/10)²⁵)/(1 - 9/10)
S = 92.82 m
Thus, the total distance the monkey has traveled when she completes her 25th swing is 92.82 m if the monkey is swinging from a tree. On the first swing, she passes through an arc of 10 m. With each swing, she passes through an arc 9/10 the length of the previous swing.
Learn more about the sequence here:
brainly.com/question/21961097
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