Let d be the common difference of the given sequence.
Given that,
[tex]\begin{gathered} a_{12}=87 \\ a_{20}=135 \end{gathered}[/tex]By definition,
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ d=\frac{a_n-a_1}{n-1} \end{gathered}[/tex]For, n = 12,
[tex]d=\frac{87-a_1}{11}[/tex]For, n = 20,
[tex]d=\frac{135-a_1}{19}[/tex]Therefore,
[tex]\begin{gathered} \frac{87-a_1}{11}=\frac{135-a_1}{19} \\ 1653-19a_1=1485-11a_1 \\ 8a_1=168 \\ a_1=21 \end{gathered}[/tex]Therefore, common difference,
[tex]\begin{gathered} d=\frac{87-21}{11} \\ =\frac{66}{11} \\ =6 \end{gathered}[/tex]Therefore, common difference is 6.
