$5^{th}$ degree polynomial expression 
$p(x)$ is a $5$ degree polynomial such that
$p(1)=1,p(2)=1,p(3)=2,p(4)=3,p(5)=5,p(6)=8,$ then $p(7)$

$\bf{My\; Try::}$ Here We can not write the given polynomial as $p(x)=x$
and $p(x)=ax^5+bx^4+cx^3+dx^2+ex+f$ for a very complex system of equation,
plz hel me how can i solve that question, Thanks

Assume $p(x)$ of the form
$$p(x)=a\prod_{r=1}^5(x-r)+b\prod_{r=1}^4(x-r)+c\prod_{r=1}^3(x-r)+d\prod_{r=1}^2(x-r)+e(x-1)+f$$ Now put the values of $x$ i.e. $x=1,2,3,4,5,6$ , then values of $a,b,c,d,e,f$ will be $[\frac{-1}{40},\frac{1}{12},\frac{-1}{6},\frac{1}{2},0,1]$ respectively. you can get these values very easily and with alomost no calculation. Start with $x=1$ and get the value  of $f$ and then put more values to get $b,c,d,e,f$
So  $p(7)=8$
Hope this will help as this method does not solves the complicated equations.
