Question

A bricklayer builds a triangular wall with layers of bricks as shown. if the bricklayer uses 171 bricks, how many layers did he build?

Answer 1

$S_x=\frac{x}{2}[2a+(x-1\left)d\right]$

Where $a$ is the first term in sequence

$171=\frac{x}{2}[2\times 1+(x-1)\times 1]171=\frac{x}{2}[2+x-1]342=x^2+x{x}^2+n-342=0x^2+n-342=0x^2+19x-18x-342=0x(x+19)-18(x+19)=0x=(-19,18)$

Obviously it cannot be negative so answer is $18$