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Re: Algebra
The topmost layer in the pile contains 1 pole, the 2nd layer 2 poles, the third layers 3 poles, and so on. The bottom-most layer, say nth layer, contains n posts.
$1 + 2 + 3 ~ + ... + ~ 5 ~ + ... + ~ n$
The number of poles in these layers of piles is in the form of arithmetic progression (AP) with a common difference d of 1. The first term a1 in AP is 1 (for topmost layer) and the number of terms in AP is the number of layers in the pile. The formula is given by
$S = \frac{1}{2}n[ \, 2a_1 + (n - 1)d \, ]$
$1275 = \frac{1}{2}n[ \, 2(1) + (n - 1)(1) \, ]$
$2550 = 2n + n(n - 1)$
$2550 = 2n + n^2 - n$
$n^2 - n - 2550 = 0$
$(n - 51)(n + 50) = 0$
$n = 51 ~ \text{and} ~ -50$
There are 51 layers in the pile.