If f(1)=6 and f(n)=-5f(n-1)-4 then find the value of f(5)

3126

Step-by-step explanation: f(1)=6 and f(n)=5f(n-1)-4. This means that next number is 5 times previous number minus 4.

f(2)=5f(1)-4 =5x6-4 = 30-4 = 26

f(3)=5f(2)-4 =5x26-4 = 130-4 = 126

f(4)=5f(3)-4 =5x126-4 = 630-4 = 626

f(5)=5f(4)-4 =5x626-4 = 3130-4 = 3126

The fifth term of the sequence is 4166

Given the recursive function expressed as;

f(n)=-5f(n-1)-4

If f(1 ) = 6

f(2) = -5f(1) - 4

f(2) = -5(6) - 4

f(2) = -30 - 4

f(2) = -34

If n = 3

f(3) = -5f(2) - 4

f(3) = -5(-34) - 4

f(3) = 170 - 4

f(3) = 166

If n = 4

f(4) = -5f(3) - 4

f(4) = -5(166) - 4

f(4) = -830 - 4

f(4) = -834

If n = 5

f(5) = -5f(4) - 4

f(5) = -5(-834) - 4

f(5) = 4170 - 4

f(5) = 4166

Hence the fifth term of the sequence is 4166

Learn more on recursive function here: link

3

step-by-step explanation: