Question

If f ( 1 ) = 5 f(1)=5 and f ( n ) = − 2 f ( n − 1 ) − 5 f(n)=−2f(n−1)−5 then find the value of f ( 4 ) f(4).

Answer 1

Using the recursive formula provided, f(4) is calculated step by step. Starting with the base value, we find f(2), then use that to find f(3), and finally f(4), which is -55.

Step-by-step explanation:

To find the value of f(4), we will use the recursive definition provided where f(1) = 5 and f(n) = -2f(n-1) - 5. First, find the value of f(2) by substituting n = 2 into the recursive formula:

• f(2) = -2f(2-1) - 5 = -2f(1) - 5 = -2(5) - 5 = -15

Next, find the value of f(3):

• f(3) = -2f(3-1) - 5 = -2f(2) - 5 = -2(-15) - 5 = 25

Finally, find the value of f(4):

• f(4) = -2f(4-1) - 5 = -2f(3) - 5 = -2(25) - 5 = -55

Answer 2

f(4) = -55

Step-by-step explanation:

Given

f(1) = 5

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

If you substitute n with 4 you get:

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

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

= -2f(3) - 5

This shows that you have to calculate the value of f(3) before we can get the value of f(4). To calculate f(3) we have to know f(2) and to calculate f(2) we have to know f(1), which is given.

Let's start from the bottom.

f(1) = 5

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

= -2f(2-1) - 5

= -2f(1) - 5 // substitute f(1) with the value 5 (given)

= -2(5) - 5

= -15

f(3) = -2f(n-1) - 5

= -2f(3-1) - 5

= -2f(2) - 5

= -2(-15) - 5

= 25

Now we can finally calculate f(4)!

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

= -2f(4-1) - 5

= -2f(3) - 5

= -2(25) - 5

= -55