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Telephone poles are stored in a pile with 30 poles in the first layer, 29 in the second, and so on. If there are 12 layers, how many telephone poles does the pile contain?

Respuesta :

Answer: 294

Step-by-step explanation:

Given

First layer has 30 Poles

Second layer has 29 Poles

There are twelve layers

It follows an A.P. with first term [tex]a_1=30[/tex] and common difference [tex]d=-1[/tex]

Sum of n terms of an A.P. is

[tex]\Rightarrow S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

Insert the values

[tex]\Rightarrow S_n=\dfrac{12}{2}[2\times 30+(12-1)(-1)]\\\\\Rightarrow S_n=6[60-11]\\\Rightarrow S_n=294[/tex]

So, there are 294 Poles in 12 layers