Suppose that you are responsible for predicting the cost of constructing a new office building. You find that the first story costs 500 dollars per square meter of floor space, and the second story costs 600 dollars per square meter. Assume that the costs per square meter form a geometric sequence.
a. Find the cost of the 10th story.
b. Write the equation that corresponds with this problem
r = 600/500 = 1.2
T10 = 500*1.2^9 = 2580
Tn = 500*1.2^(n-1)
To find the cost of the 10th story, we need to determine the common ratio of the geometric sequence. Since the cost of the first story is $500 per square meter and the cost of the second story is $600 per square meter, we can calculate the common ratio by dividing the cost of the second story by the cost of the first story.
Common ratio (r) = Cost of the second story / Cost of the first story
= $600 / $500
= 1.2
Now that we have the common ratio, we can use the formula for the nth term of a geometric sequence to find the cost of the 10th story.
The formula for the nth term of a geometric sequence is:
An = A1 * r^(n-1)
Where:
An = nth term
A1 = first term
r = common ratio
n = position of the term
Using this formula, we can substitute the values to find the cost of the 10th story.
a. Cost of the 10th story:
A10 = $500 * (1.2)^(10-1)
= $500 * (1.2)^9
To evaluate this expression, calculate the value of (1.2)^9 and multiply it by $500.
b. The equation that corresponds with this problem is:
An = $500 * (1.2)^(n-1)
This equation represents the cost of the nth story in the office building, where n represents the position of the story.