SOLUTION: In a certain spider web, the lengths of the shortest and longest threads are 3.4mm and 50.2mm respectively. The successive equally spaced threads are 1.2mm apart. If the length of
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Question 1203960: In a certain spider web, the lengths of the shortest and longest threads are 3.4mm and 50.2mm respectively. The successive equally spaced threads are 1.2mm apart. If the length of the cross threads form an Arithmetic Progression (A.P), find the number of cross threads. Found 2 solutions by mananth, greenestamps:Answer by mananth(16946) (Show Source):
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In a certain spider web, the lengths of the shortest and longest threads are 3.4mm and 50.2mm respectively. The successive equally spaced threads are 1.2mm apart. If the length of the cross threads form an Arithmetic Progression (A.P), find the number of cross threads.
Length of the shortest thread are 3.4mm
Length of the longest thread are 50.2mm
The successive equally spaced threads are 1.2mm apart
length of the cross threads form an Arithmetic Progression
Here a 3.4 , tn = 50.2 d= 1.2
tn = a+(n-1)*d
50.2= 3.4+ (n-1)* 1.2
50.2 - 3.4 = (n-1)*1.2
46.8= (n-1) *1.2
46.8/1.2= n-1
39 = n-1
n=40
The number of cross threads =40
You should understand the formal algebra that can be used to solve the problem, as shown in the response from the other tutor. But I believe students will understand how to work problems involving arithmetic progressions better if they are able to work the problem informally -- which helps them understand WHY the formal algebra works.
If we subtract the shortest thread length from the longest and divide the result by the difference between the lengths of successive threads, we get the number of threads AFTER THE FIRST ONE.
