To describe a specific arith-metic sequence, Elijah wrotethe recursive formula:[ f(0) = 30f(n+1)=f(n)+7Write a linear equation thatmodels this sequence

Answer:[tex]f(x) = 7x + 30[/tex]Step-by-step explanation:We need at least two points to write the equation of a straight line.The recursive formula that Elijah wrote is:[tex]f(0) = 30[/tex][tex]f(n + 1) = f(n) + 7[/tex]When we substitute n=0, we get:[tex]f(0 + 1) = f(0) + 7[/tex][tex]f(1) = 30 + 7[/tex][tex]f(1) = 37[/tex]The points (0,30) and (1,37) lies on this line.The equation of this line is of the form:[tex]f(x) = mx + b[/tex]where b =30 is the y-intercept and m=7 is the slope.We plug in these values to get:[tex]f(x) = 7x + 30[/tex]Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.You could also use the two points to find the slope:[tex]m = \frac{37 - 30}{1 - 0} = 7[/tex]