the distances of a port from 20 different locations from an arithmetic progression. If the farthest distance is 300 km, and the nearest distance is 30 km, what is the distance between any two successive locations? .
Pls i haven't seen the answer
The distance of a port form 20 difference location form an AP. if the farthest distance is 300km and the nearest distance is 30km what is the distance between any two successive location
To find the distance between any two successive locations, we first need to determine the common difference in the arithmetic progression.
The farthest distance is 300 km, and the nearest distance is 30 km.
Let's assume the nearest distance is the first term (a) and the common difference is (d).
So, a = 30 km and a + (19 * d) = 300 km.
From the second equation, we can solve for d:
30 + 19d = 300
19d = 270
d = 270/19
d ≈ 14.21 km (rounded to two decimal places)
Therefore, the distance between any two successive locations is approximately 14.21 km.
To find the distance between any two successive locations, we need to determine the common difference of the arithmetic progression.
Given that the farthest distance from the port is 300 km and the nearest distance is 30 km, we have two terms of the arithmetic progression, namely a1 = 30 km and a20 = 300 km.
We can use the formula for the nth term of an arithmetic progression to find the common difference (d):
a_n = a_1 + (n-1)d
For the first term (a_1 = 30 km), we have n = 1:
30 km = 30 km + (1-1)d
0 = d
Therefore, d = 0.
However, having a common difference of 0 would mean that all the distances are equal, which contradicts the given information. Thus, it is not possible for the given distances to form an arithmetic progression.
Without further information, we cannot determine the distance between any two successive locations.