[tex]\begin{gathered} \text{fourth term}\rightarrow8 \\ \text{fifth term}\rightarrow11 \end{gathered}[/tex]
Explanation
An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term,it is give by the expression:
[tex]a_n=a_1+(n-1)d[/tex]
so
Step 1
use the given data to find the arithmetic sequence
so
let
[tex]\begin{gathered} a_1=-1 \\ a_2=2 \\ a_3=5 \end{gathered}[/tex]
so
a) find the common difference
[tex]\begin{gathered} \text{Difference}_1=a_2-a_1=2-(-1)=2+1=3 \\ \text{Difference}_1=5-2=3 \\ \end{gathered}[/tex]
hence the common difference is 3
[tex]d=\text{ 3}[/tex]
now, chec the first term and replace in the formula
[tex]\begin{gathered} \text{first term}\rightarrow-1 \\ \text{difference}\rightarrow3 \\ \text{replace} \\ a_n=a_1+(n-1) \\ a_n=-1+(n-1)3 \end{gathered}[/tex]
Step 2
now, use the expression to find teh netx two terms
a)
[tex]\begin{gathered} a_n=-1+(n-1)3 \\ \text{for n= 4,replace} \\ a_4=-1+(4-1)3 \\ a_4=-1+(3)3=-1+9=8 \\ a_4=8 \end{gathered}[/tex]
b) fifth term
[tex]\begin{gathered} a_n=-1+(n-1)3 \\ \text{for n= 4,replace} \\ a_5=-1+(5-1)3 \\ a_5=-1+(4)3=-1+12=11 \\ a_5=11 \end{gathered}[/tex]
so, the answer is
[tex]8,11[/tex]
I hope this helps you
