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The total height climbed is 450 feet if a rock climber climbs 90 feet of the steep rock face in the first half-hour of climbing. In each succeeding half-hour, the climber achieves only 80% of the height achieved in the previous half-hour
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 rock climber climbs 90 feet of the steep rock face in the first half-hour of climbing.
In the second half rock climber climbed = 80% of 90 = 72 ft
In the third half hour = 80% of 72 = 57.6 ft
In the fourth half = 80% of 57.6 = 46.08 ft
We have a geometric progression:
90, 72, 57.6, 46.08.... infinitely
Here the common ratio r = 72/90 = 0.8
The sum of the infinite series of a GP = a/(1-r)
= 90/(1-0.8)
= 450 feet
Thus, the total height climbed is 450 feet if a rock climber climbs 90 feet of the steep rock face in the first half-hour of climbing. In each succeeding half-hour, the climber achieves only 80% of the height achieved in the previous half-hour
Learn more about the sequence here:
brainly.com/question/21961097
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