To begin, let's observe the given terms in the sequence to determine the value of the first term as well as the common difference. $-11→−4-15→−4-19→−4-23 $ We can use this information to write an equation for the $n_{th}$ term of the sequence.
When graphing a sequence, the $x-$axis always represents the number of the term $n$ and the $y-$axis represents the value of the term $a_{n}.$
$n$ | $-4n−7$ | $a_{n}$ | $(n,a_{n})$ |
---|---|---|---|
$1$ | $-4(1)−7$ | $-11$ | $(1,-11)$ |
$2$ | $-4(2)−7$ | $-15$ | $(2,-15)$ |
$3$ | $-4(3)−7$ | $-19$ | $(3,-19)$ |
$4$ | $-4(4)−7$ | $-23$ | $(4,-23)$ |
$5$ | $-4(5)−7$ | $-27$ | $(5,-27)$ |
Now let's graph these points on a coordinate plane.