Solution:
[tex]\begin{gathered} a_1=21 \\ a_{83}=513 \end{gathered}[/tex]
The nth term of an arithmetic seuence is
[tex]\begin{gathered} a_n=a+(n-1)d \\ a_{83}=21+(83-1)d \\ 513=21+82d \\ 513-21=82d \\ 82d=492 \\ \frac{82d}{82}=\frac{492}{82} \\ d=6 \end{gathered}[/tex]
To figure out the 35th term, we will use the formula below
[tex]\begin{gathered} a_{35}=a_1+(n-1)d \\ a_{35}=21+(35-1)6 \\ a_{35}=21+204 \\ a_{35}=225 \end{gathered}[/tex]
Hence,
The final answer is
[tex]a_{35}\Rightarrow225[/tex]
