Question

Find the next term in this arithmuc sequence

Answer 1

Hey there :)

$\frac{7}{2}, \frac{9}{4},1, -\frac{1}{4} , -\frac{3}{2} , \frac{?}{?}$

We can find the common difference here as it is an arithmetic sequence.

The common difference between each term is: $\frac{5}{4}$

$\frac{7}{2} - \frac{5}{4} = \frac{9}{4}$

We can find the unknown term by:
$-\frac{3}{2}- \frac{5}{4}= -\frac{11}{4}$ {easier way in this example}

OR

by the formula for finding the nth term

a₆ = $\frac{7}{2} +(6-1)( -\frac{5}{4} )$ 
{a₆ because it is the 6th term to be found, (6-1) the nth term minus 1}

a₆ = $- \frac{11}{4}$
However this way is not essential here as the previous term is given.