Substitute the common difference and the first term of the sequence into the formula and simplify. SolutionThe common difference can be found by subtracting the first term from the second term. Write an explicit formula for the arithmetic sequence. ĥ Writing the Term Explicit Formula for an Arithmetic Sequence Substitute the common difference and the first term into.Given the first several terms for an arithmetic sequence, write an explicit formula. Įxplicit Formula for an Arithmetic SequenceĪn explicit formula for the term of an arithmetic sequence is given by Another explicit formula for this sequence is, which simplifies to. We do not need to find the vertical intercept to write an explicit formula for an arithmetic sequence. Substituting for the slope and for the vertical intercept, we get the following equation: If we know the slope and vertical intercept of the function, we can substitute them for and in the slope-intercept form of a line. When dealing with sequences, we use in place of and in place of. Recall the slope-intercept form of a line is. You can also find the -intercept by graphing the function and determining where a line that connects the points would intersect the vertical axis. To find the -intercept, we subtract from. The common difference is, so the sequence represents a linear function with a slope of. To find the y-intercept of the function, we can subtract the common difference from the first term of the sequence. We can construct the linear function if we know the slope and the vertical intercept. The common difference is the constant rate of change, or the slope of the function. We can think of an arithmetic sequence as a function on the domain of the natural numbers it is a linear function because it has a constant rate of change.
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