1003107307

We are given a sequence \( \left( a_n \right)^{\infty}_{n=1} \) defined recursively by: \( a_1=1,\ a_2=5\) and \(\ a_{n+2}=a_{n+1}-a_n+d\), where \(\ n\in\mathbb{N} \). Find the value of an unknown constant \( d\in\mathbb{R} \) and of the term \( a_5 \) if \( a_3 = 10 \).