Question

Finish the pattern with a mixed number, 2 1/2, 3 3/4, , __

Answer 1

We have a series: 2 1/2, 3 3/4, ...

We can consider this is a arithmetic series, so it has a common difference. This difference can be calculated as:

`\begin{gathered} d=a_2-a_1 \\ d=(3+(3)/(4))-(2+(1)/(2)) \\ d=3-2+(3)/(4)-(1)/(2) \\ d=1+(3-2)/(4) \\ d=1+(1)/(4) \end{gathered}`

We then can consider that each term adds 1 1/4 to the previous term.

We can calculate the third and fourth term of the series as:

`\begin{gathered} a_3=a_2+d \\ a_3=3+(3)/(4)+1+(1)/(4)=3+1+(3+1)/(4)=4+(4)/(4)=4+1=5 \end{gathered}`
`\begin{gathered} a_4=a_3+d \\ a_4=5+1+(1)/(4)=6+(1)/(4) \end{gathered}`

Answer: the third term is 5 and the fourth term is 6 1/4.