Solve for the following two recurrence equations:

If $T(0)=5$ and $T(n)=T(n-3)+10,$ solve for $T(n)$ in terms of $n.$

If $T(0)=1$ and $T(n)=T(n-1)+n,$ solve for $T(n)$ in terms of $n.$

Write the recursive equation for the run time of the following static method and solve the equation in terms of $n.$

public static int method $($String $s,$ char $c)$

$\{$

int $n=s.$ length$()$;

String $s1$;

if $)<mi\; id="EditorElement\_2012739">(</mi><mn\; id="EditorElement\_2012733">1</mn>$

return $-1$; $//$ not found

else

if $(s*charAt(n-1)==c$

return $n-1$;

else

$\{$

s$1=$ s$.$substring $(0,n-1)$;

return method $(s1,c)$;

$\}$

$\}$