Answer:
Term Result
123 724
250 1486
Explanation:
A table of the values is attached (Table1). The puropose of a table in this case is help identify the relationship between the series of numbers. The first column is added to label the term number, starting from 0. The question eventually asks for the value of 123rd and 250th terms, so it seems a good idea to incorporate term numbers early in the analysis.
The table suggests a pattern in the sequence. There is a constant difference of +6 each time the term increases by 1 (Column 3). This measn there is a linear relationship. The term column in the table can be increased as far down as we want, even to 250. With a spreadshhet, this is a simple task. A more useful, and elegant, approach is to derive the linear equation that will predict the value of any term, which we'll call x. The result of the term is y.
y = mx + b is the satadrad format of a linear equation: m is the slope (or rate of change) and b is the y-intercept (the value of y when x = 0). We have what we need to find both m and b.
m is the change between consequtive terms, which is 6 (y increases by 6 for every consecutive term). The value of b is -14, since a term of 0 results in a -14.
The linear equation is thus: y = 6x-14, where x is the term and y the result. The third column (Predict) shows the results for the terms provided, and includes the predictions for terms 123 and 250. The equations correctly predicts the given terms, so we can felel confident that any term can be determined with y = mx - 14.
Term Result
123 724
250 1486