Answer:
Given, \[{{a}_{21}}-{{a}_{7}}=84\] \[\Rightarrow \] \[(a+20d)-(a+6d)=84\] \[\Rightarrow \] \[a+20d-a-6d=84\] \[\Rightarrow \] \[20d-6d=84\] \[\Rightarrow \] \[14d=84\] \[\Rightarrow \] \[d=\frac{84}{14}=6\] Hence common difference \[=6\].
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