Hey there :)
[tex] \frac{7}{2}, \frac{9}{4},1, -\frac{1}{4} , -\frac{3}{2} , \frac{?}{?} [/tex]
We can find the common difference here as it is an arithmetic sequence.
The common difference between each term is: [tex] \frac{5}{4} [/tex]
[tex] \frac{7}{2} - \frac{5}{4} = \frac{9}{4} [/tex]
We can find the unknown term by:
[tex] -\frac{3}{2}- \frac{5}{4}= -\frac{11}{4} [/tex] {easier way in this example}
OR
by the formula for finding the nth term
a₆ = [tex] \frac{7}{2} +(6-1)( -\frac{5}{4} )[/tex]
{a₆ because it is the 6th term to be found, (6-1) the nth term minus 1}
a₆ = [tex]- \frac{11}{4} [/tex]
However this way is not essential here as the previous term is given.
