Question

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?

Answer 1

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 $a_1=30$ and common difference $d=-1$

Sum of n terms of an A.P. is

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

Insert the values

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

So, there are 294 Poles in 12 layers