if f(n)=f(n-1)+7 and f(1)=-18 then f(37) =?

Question

i have four choices, but i don't know where to begin, except to work backward and plug in the answers.  i would like to understand without getting choices

Answer 1

This one is simple! But remember, simple doesn't always mean EASY. Hopefully after this walkthrough it is simple and easy. 

 

f(n) = f(n-1) + 7 is a recursive function because it includes the f(n-1), which is just the previous term.

 

so, let's apply the f(1) = -18 information like this:

 

f(1) = -18 = f(0) + 7   ««  note: f(n-1) = f(0) because n=1

 

-18 = f(0) +7   ⇒  f(0) = -25

 

notice, this tells us that we just have to add 7 to get to the next term of the sequence.

 

 

SO, NOW WE KNOW WHAT TO DO!!! Just add 7 to each term in order to get to the next.

Lastly, I will spell out how to reach the actual answer!

 

f(0) = -25

f(1) = -18

f(2) = -11

f(3) = -4

.

.

.

f(37) = 

 

of course, you could also express it as a linear equation... i.e. try using f(x) = mx + b

 

Kevin G.

Wyzant Tutor (specializing in all math, physics, chemistry, and much more!!!)

 

Answer 2

f(2) = f(2 - 1) + 7 = -18 + 7 = -11

f(3) = f(3 - 1) + 7 = -11 + 7 = -4

f(4) = f(4 - 1) + 1 = -4 + 7 = 3

 

As you can see, this pattern is recursive.  You will need to add 7 to the previous term 33 times to obtain f(37), using this pattern.

Answer 3

f(n)=f(n-1)+7 and f(1)=-18

let n=2

f(2)=f(2-1)+7

f(2)=f(1)+7

f(2)=-18+7

f(2)=-11

the sequence is -18, -11, -4, 3, 10, 17, ...

f(37)=a+d(n-1) where a=first term and d=common difference

f(37)=-18+7(37-1)

f(37)=-18+7(36)

f(37)=-18+252

f(37)=234