Please ExplainGiven the formula for an arithmetic sequence f(6) = f(5) + 3 written using a recursive formula, write the sequence using an arithmetic formula. f(6) = f(1) + 3 f(6) = f(1) + 12 f(6) = f(1) + 15 f(6) = f(1) + 18

Answer:f(6)=f(1)+15Step-by-step explanation:Ok if f(6)-f(5)=3, then f(n)-f(n-1)=3 for any integer n greater than or equal to 2.f(6)-f(1)=(f(6)-f(5))+(f(5)-f(4))+(f(4)-f(3))+(f(3)-f(2))+(f(2)-f(1))=(3)         + (3)         +(3)         +(3)         +(3)=5(3)=15So the answer is the third one:f(6)=f(1)+15Arithmetic sequences are linear.So no matter the points we choose, we should get the same slope.[tex]\frac{f(6)-f(5)}{6-5}=\frac{f(6)-f(1)}{6-1}=3[/tex]Both slopes are 3 since we were given term-previous term is 3.[tex]\frac{f(6)-f(1)}{6-1}=3[/tex][tex]\frac{f(6)-f(1)}{5}=3[/tex]Multiply both sides by 5:[tex]f(6)-f(1)=5(3)[/tex][tex]f(6)-f(1)=15[/tex][tex]f(6)=f(1)+15[/tex]