Enzo’s profit over the last few months has been falling. In December he made $900, in January his profit was $500, and in March, he lost $300. Is the sequence that represents his profit arithmetic? If it is, what is the recursive formula for the sequence?

Accepted Solution

Answer:See explanationStep-by-step explanation:Enzo’s profit over the last few months:In December, he made profit $900;In January, his his profit was $500; In February - unknown;In March, his loss was  $300.Find the difference between given dataDec - Jan [tex]\$900-\$500=\$400[/tex]Jan - Feb [tex]\$500-\$x[/tex]Feb - Mar [tex]\$x-(-\$300)=\$x+\$300[/tex]If this sequence is arithmetic, then [tex]\$500-\$x=\$x+\$300=\$400\\ \\\$x=\$100[/tex]So, if the profit in February was $100, then this sequence is arithmetic sequence. In this case,[tex]a_1=900\\ \\a_2=500\\ \\a_3=100\\ \\a_4=-300\\ \\...\\ \\d=-400[/tex]The recursive formula is[tex]a_n=a_{n-1}-400[/tex]