question_answer

What is the common difference of an A.P in which \[{{a}_{21}}-{{a}_{7}}=84\]?

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 \[=6\].