Given the formula for an arithmetic sequence f(9) = f(8) + 5 written using a recursive formula, write the sequence using an arithmetic formula. f(9) = f(1) + 5 f(9) = f(1) + 30 f(9) = f(1) + 35 f(9) = f(1) + 40

Answer:f(9)=f(1)+40Step-by-step explanation:We are given term=previous term+5 by the equation f(9)=f(8)+5 and that the sequence is arithmetic.This tells the slope of the line is 5. (We know it is linear because it is arithmetic).So we want to find the slope of the line going through (1,f(1)) and (9,f(9)).[tex]\frac{f(9)-f(1)}{9-1}=5[/tex][tex]f(9)-f(1)=5(9-1)[/tex][tex]f(9)-f(1)=5(8)[/tex][tex]f(9)-f(1)=40[/tex]