Find a28 in the arithmetic sequence: 5.8, 3.5, 1.2, -1.1,

Answer:-56.3Step-by-step explanation:We don't have to much guessing because it tells us it is arithmetic which means it has a common difference.That is a term minus it's previous will be the same.[tex]3.5-5.8=-2.3[/tex][tex]1.2-3.5=-2.3[/tex][tex]-1.1-1.2=-2.3[/tex]In general:[tex]a_n-a_{n-1}=-2.3[/tex] with [tex]a_1=5.8[/tex] if you wanted the recursive form.You can also find the explicit form which would be more helpful for our task of finding the 28th term.[tex]a_n=a_1+d(n-1)[/tex] is the explicit form where [tex]d[/tex] is the common difference and [tex]a_1[/tex] is the first term.Inputting -2.3 for [tex]d[/tex] and 5.8 for [tex]a_1[/tex]:[tex]a_n=5.8+-2.3(n-1)[/tex]Now the 28th term or [tex]a_{28}[/tex] can be found by replacing n with 28:[tex]a_{28}=5.8+-2.3(28-1)[/tex][tex]a_{28}=5.8+-2.3(27)[/tex][tex]a_{28}=-56.3[/tex]