Mathematics: If f(1)=10 and f(n)=-5f(n-1)-2 then find the value of f(4)

The length of the cable is Step-by-step explanation:Letx----- the length of the cablewe know that...

If f(1)=10 and f(n)=-5f(n-1)-2 then find the value

Ответ:

Mrlittlefish

09.01.2022

Mathematics

$\large\boxed{f(4)=-1292}$

Step-by-step explanation:

$f(n)=-5f(n-1)-2\\\\f(1)=10\\\\f(2)=-5f(2-1)-2=-5f(1)-2\\\text{put}\ f(1)=10:\\f(2)=-5(10)-2=-50-2=-52\\\\f(3)=-5f(3-1)-2=-5f(2)-2\\\text{put}\ f(2)=-52\\f(3)=-5(-52)-2=260-2=258\\\\f(4)=-5f(4-1)-2=-5f(3)-2\\\text{put}\ f(3)=258\\f(4)=-5(258)-2=-1290-2=-1292$