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Thermal treatment by pyrolysis has been proposed as a sustainable alternative to enable the agricultural use of sewage sludge. The solid product obtained via pyrolysis of sewage sludge is called sewage sludge biochar and presents several advantages for its use as a fertilizer or soil conditioner. However, there are concerns about the accumulation and dynamics of trace elements in soil amended with sewage sludge biochar over the years. This study examined the effect of sewage sludge biochar, under field conditions for 5 yr, on the accumulation and availability of trace elements in a tropical soil. For this, 15 t ha–1 of sewage sludge biochar produced at 300 and 500 °C were applied in the first two growing seasons. Application was interrupted from the third to the fifth seasons to assess the residual effect of sewage sludge biochar in the soil. The total and available trace element concentrations were determined. The total contents of trace elements showed the following variation in the soil over the 5 yr (mg kg–1): Cd (16.8–20.0), Co (19.5–21.5), Cr (98.2–125.7), Cu (8.1–17.1), Mn (62.9–85.7), Ni (20.3–35.0), Pb (27.0–52.4), and Zn (20.3–35.8). There was no change in the availability of Cd, Cr, Ni, and Pb over the years. Additionally, a residual effect of the sewage sludge biochar was the increase in availability of trace elements that are considered essential (Cu, Mn, and Zn) and beneficial elements (Co) for plants. Therefore, in relation to contamination by trace elements, the pyrolysis of sewage sludge of domestic origin proved to be an adequate strategy to enable the safe use of this residue in tropical agriculture.

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In everyday life it is common to deal with some situations that involve the need to determine a general rule to describe them. To help in the description of phenomena that involve quantities that can be expressed in terms of polynomial functions, there is a need to find instruments that facilitate obtaining such polynomial functions from the data analyzed in the process. An easy way to obtain polynomial functions from a sequence of real numbers is through the study of Higher Order Arithmetic Sequences. If the sequence obtained from the data collected through an experiment is polynomial, then this sequence is called an arithmetic sequence of order k, where k is the degree of the polynomial. With the study of higher order arithmetic sequences it is possible to obtain from a sequence of real numbers both the formula that describes this sequence and the formula for the sum of the first n terms of this sequence. With this, we will be able to obtain general formulas that allow us to obtain an estimate for the behavior of different phenomena. Thus, through the bibliographic survey, consulting the reference [1], the research project began with weekly meetings.

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