Answer:
[tex]a_{45}=221[/tex]
Step-by-step explanation:
Arithmetic sequences are represented by the following equation;
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ where, \\ a_1=\text{ first term} \\ d=\text{ common difference} \\ n=\text{ nth term} \end{gathered}[/tex]
The common difference is the difference between the consecutive terms:
[tex]\begin{gathered} d=6-1=5 \\ d=11-6=5 \\ d=16-11=5 \end{gathered}[/tex]
Therefore, the equation that represents this sequence:
[tex]a_n=1+5(n-1)[/tex]
Now, if we want to find the 45th term, substitute n=45:
[tex]\begin{gathered} a_{45}=1+5(45-1) \\ a_{45}=1+5*(44) \\ a_{45}=1+220 \\ a_{45}=221 \end{gathered}[/tex]
