This is an arithmetic sequence. The first term, [tex] a_{1} [/tex], is 27. The common difference is -3 (you subtract 3 from a number to get to the next number in line), and you are looking for term number 43, or [tex] a_{43} [/tex]. Your formula for an arithmetic sequence is [tex] a_{n}= a_{1} +d(n-1)[/tex]. If we are looking for term number 43, our first number in the sequence is 27, and the common difference is -3, then our formula is this one: [tex] a_{43} =27-3(43-1)[/tex], which simplifies to [tex]a_{43}=27-3(42)[/tex], which is [tex]a_{43}=27-126[/tex] and [tex]a_{43}=-99[/tex]
