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Question 1185764: A railroad bridge is built over a V-shaped canyon. If the supports are 3 feet long at each end, the center support is 563 feet long, and the supports increase in length by 4 feet with each support (from 3 feet to 563 feet), what is the total length of all the supports? Please show the work, thank you!
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The sum of the lengths of the supports is
3+7+11+...+559+563+559+...+11+7+3
= 2(3+7+11+...+559)+563
Find the sum of the arithmetic sequence in parentheses using
sum = number of terms times average of all the terms, or
sum = number of terms times average of first and last terms.
The number of terms is (last minus first) divided by common difference, plus 1.
(559-3)/4+1 = 139+1 = 140
The average of the first and last terms is (3+559)/2 = 281.
The sum of the lengths of the supports is then
2(140*281)+563
Use a calculator to get
ANSWER: 79,243 feet
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