Question

I really don't know how to solve this problem. Can someone please guide me through it?
http://i.imgur.com/v1gzD57.png

Answer 1

What are we doing to the first term to get the second term?

if you aren't sure, solve the following for d

7 + d = 4

Answer 2

We are removing 3

Answer 3

ie subtracting 3 each time

Answer 4

7 - 3 = 4
4 - 3 = 1
1 - 3 = -2

Answer 5

then -5, then -8 right?

Answer 6

in general, to get the next term f(n+1) you subtract 3 from the nth term

f(n+1) = f(n) - 3

Answer 7

yeah and it goes on forever

Answer 8

So it would be option C: f(1) = 7, f(n + 1) = f(n) - 4; for n ≥ 1

Answer 9

f(1) = 7 is given to us

to find f(2) we subtract off 3

or we use the formula f(n+1) = f(n) - 3


f(n+1) = f(n) - 3

f(1+1) = f(1) - 3 ... replace each n with 1

f(2) = 7 - 3

f(2) = 4

Answer 10

you'll do that for n = 2, n = 3, etc

Answer 11

I still think it's option C

Answer 12

no we aren't subtracting 4 each time

Answer 13

I don't get this at all then

Answer 14

f(1) is the first term

f(2) is the second term

f(3) is the third term

etc etc

in general, the nth term is f(n). We replace n with whole numbers like n = 5 or n = 6

Answer 15

Its A

Answer 16

jumping from 7 to 4, then to 1, etc means we subtract 3 each time

in general we have the nth term f(n) subtract off 3

f(n) - 3

Answer 17

that gives the term right after the nth term, the f(n+1) term

which is why

f(n+1) = f(n) - 3

Answer 18

look at f(n+1) = f(n) - 3

what happens when you replace every n with say n = 3

Answer 19

f(4)=f(3)-3?

Answer 20

All I did was substitute 'n' with 3

Answer 21

saying "f(3) - 3" means "take the third term and subtract off 3"

the third term is 1

so f(3) - 3 = 1 - 3 = -2 which gives us the fourth term f(4)

Answer 22

Ehh I give up on this. I'll just guess the answer because I'm still as confused as I was in the beginning. I'm sorry for completely wasting your time :/
Thank you very much though.

Answer 23

do you see how f(n) is the nth term?