hi so i am stuck at this question that is asking about arithmetic sequence .
Five fence posts are equally spaced between two corner posts that are 42 meter apart. how far apart are the five fence posts.
i know the answer is 7m but i don't know how plus i know the equation for the arithmetic sequence is
tn=t1(n-1)d, but how does it apply to this question?
a=0(starting from a corner pole1) no of poles=n=72 t7=42(corner pole 2) d=spacing 42=0+d(7-1) 6d=42 d=7m
There are 7 posts including the two end ones.
That means six equal spaces between posts
42/6 = 7 meters
(note, number of spaces = number of posts - 1)
oh my god thank you i makes sense now
To find the distance between the five fence posts, we can use the concept of an arithmetic sequence. In an arithmetic sequence, each term is obtained by adding a constant difference (d) to the previous term.
Let's break down the given information:
- There are five fence posts equally spaced between two corner posts.
- The distance between the two corner posts is 42 meters.
To find the distance between each fence post, we can divide the total distance (42 meters) by the number of intervals between the posts. In this case, there are five intervals between the fence posts.
Distance between each fence post = Total distance / Number of intervals
= 42 meters / 5 intervals
= 8.4 meters
However, we need to find the distance "apart" or between each fence post, not the distance from one post to the next. Since there are six lengths (five spaces) between the six fence posts (including the corner posts), we need to subtract the length of one fence post to find the distance between them.
Distance between the five fence posts = Distance between each post - Length of one post
= 8.4 meters - 1 post (1 post = 1 meter)
= 8.4 meters - 1 meter
= 7.4 meters
Therefore, the distance between each of the five fence posts is 7.4 meters.
Now, let's relate this to the arithmetic sequence formula you mentioned. The formula tn = t1 + (n-1)d is used to find the nth term of an arithmetic sequence, where tn represents the nth term, t1 is the first term, n is the number of terms, and d is the common difference.
In this case, we are not interested in finding a particular term of the sequence. Instead, we need to find the distance between the fence posts. So, we used a simplified approach by dividing the total distance by the number of intervals and then adjusted for the length of a single post between each space.