question_answer

Which term of the A.P. 8, 14, 20, 26, ... will be 72 more than its 41st term ?

Answer:

A. E is 8, 14, 20, 26, ....

\[a=8,d=14-8=6\]

Let                                \[{{a}_{n}}={{a}_{41}}+72\]

\[\Rightarrow \]               \[a+(n-1)d=a+40d+72\]

\[\Rightarrow \]                     \[(n-1)6=40\times 6+72\]

\[=240+72\]

\[\Rightarrow \]                          \[n-1=\frac{312}{6}=52\]

\[\Rightarrow \]            \[n=52+1={{53}^{rd}}\] term