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= 9n + 63
generate the first few terms using the recursive equation
f(1) = 72
f(2) = 72 + 9 = 81
f(3) = 81 + 9 = 90
f(4) = 90 + 9 = 99
the sequence is 72, 81, 90, 99, .....
This is an arithmetic sequence whose n th term formula is
=
+ (n - 1 )d
where is the first term and d the common difference
d = 99 - 90 = 90 - 81 = 81 - 72 = 9 and = 72
= 72 + 9(n - 1) = 72 + 9n - 9 = 9n + 63 ← explicit formula
Answer:
The walk will cost $8164.
Step-by-step explanation:
Given:
Diameter of the circular pond (D) = 24 yd
Width of the gravel path (x) = 2 yd
Cost per yard of the path = $50
Now, radius of the circular pond is half of the diameter and is given as:
Now, area of the pond is given as:
Area of the complete path including the pond area is given as:
Now, area of the gravel path can be obtained by subtracting the pond area from the total outer area. This gives,
Now, using unitary method,
Cost of 1 square yard of path = $50
∴ Cost of 163.28 square yard of path = 50 × 163.28 = $8164
Hence, the walk will cost $8164.