Question

help me please... i really need it

The first four terms of a sequence are shown below:

6, 2, -2, -6

Which of the following functions best defines this sequence?

f(1) = 6, f(n + 1) = f(n) + 4; for n ≥ 1

f(1) = 6, f(n + 1) = f(n) - 2; for n ≥ 1

f(1) = 6, f(n + 1) = f(n) - 4; for n ≥ 1

f(1) = 6, f(n + 1) = f(n) + 2; for n ≥ 1

Answer 1

d=a(n) - a(n-1) = a2 - a1 = 2 - 6 = -4

Answer 2

The difference is -4.

Answer 3

how did you get that

Answer 4

@SolomonZelman

Answer 5

When you are given a sequence look for a pattern.
6, 2, -2, -6

What can we do to the first number to get the second number?

Answer 6

subract 4?

Answer 7

Now try to do the same to the second number and see if it gives you the third number.

Answer 8

yes it gave me the third

Answer 9

and the last

Answer 10

How about from third to fourth? Is it still the same epattern?

Answer 11

yes

Answer 12

Okay. The pattern is always subtract 4 from the current number to get the next number.

If the current number is f(n), then to get the next number, f(n+1), I need to subtract 4 from f(n). So, f(n+1) = f(n) - 4

Answer 13

Think of f(n) as a function that will give me the nth number. If I wanted the 4th number I will put n = 4 and it will give me the 4th number in the sequence.

Answer 14

so would it be f(4)?

Answer 15

Let us find the 4th number in the sequence using the formula we found.
We are interested in finding f(4).
The formula we have is: f(n+1) = f(n) - 4
If we want f(4), we need to put n = 3 so the LHS will be f(4).
put n = 3 in the formula:
f(4) = f(3) - 4
So the formula does not give you the 4th number right away but it gives the fourth number in terms of the third number. No problem. Just keep using the same formula to find f(3).

Answer 16

f(n+1) = f(n) - 4
put n = 3
f(4) = f(3) - 4
Find f(3)
put n = 2
f(3) = f(2) - 4
find f(2)
put n = 1
f(2) = f(1) - 4
We can't go back any further because the first term is reached at f(1). So we have to know what f(1) is. So when we derived the formula f(n+1) = f(n) - 4 we must say f(1) = 6. With just the formula and the starting number we can find the 4th tern or the 100th term or the 562nd term in the sequence by using the formula again and again.

Earlier we had: f(2) = f(1) - 4 = 6 - 4 = 2
f(3) = f(2) - 4 = 2 - 4 = -2
f(4) = f(3) - 4 = -2 - 4 = -6

Answer 17

So the formula is: f(n+1) = f(n) - 4 and f(1) = 6 and the formula is good for all n >= 1.

Answer 18

thankyou so much