## Precalculus: Mathematics for Calculus, 7th Edition

İn order a sequence to be arithmetic : $a_{n+1}-a_{n}=a_{n}-a_{n-1}\Rightarrow 2a_{n}=a_{n+1}+a_{n-1}$ So: $a_{n+1}+a_{n-1}=4+2^{n+1}+4+2^{n-1}=8+2^{n+1}+2^{n-1}$ $2a_{n}=2\left( 4+2^{n}\right) =8+2^{n+1}$ As we see from above $a_{n+1}+a_{n-1}\neq 2a_{n}$ So this sequence is not arithmetic