Please Help Me Check My Work :)
1) Find the 5th term of - f(n)= 3(n-3)
My answer- -279
2) Find the third term if the first term is 4 - f(n)= 2f(n-1)+2
My answer- 16
3) Find the third term using the explicit rule - f(n) 4-n/n+3
My answer- 1/6
4) Recursive Function- 1, -2, -5, -8 Find the next 4 numbers and find the function.
My answer- Sequence= 4-3n ; next 4 numbers = 28, -80, 244, -728
Thank you!!
#1 If you mean
f(n) = 3(n-3) then f(5) = 3(5-3) = 6
f(n) = 3^(n-3) then f(5) = 3^2 = 9
f(n) = 3^n - 3 then f(5) = 3^5-3 = 240
How did you come up with 279?
#2
f(n) = 2f(n-1)+2
f(1) = 4
f(2) = 2(4)+2 = 10
f(3) = 2(10)+2 = 22
#3 f(n) = (4-n)/(n+3)
f(3) = (4-3)/(3+3) = 1/6
#4 I like 4-3n
But, that means each term is just 3 less than the previous one:
1 -2 -5 -8 -11 -14 -17 ...
Your numbers appear to be 1-(-3)^n
1) To find the 5th term of the sequence f(n) = 3(n-3), you can substitute n = 5 into the equation and evaluate it.
f(5) = 3(5-3) = 3(2) = 6
So, the 5th term of the sequence is 6, not -279.
2) In order to find the third term of the sequence f(n) = 2f(n-1) + 2, you need to first determine the value of the second term. The first term is given as 4, so you can calculate the second term as follows:
f(2) = 2f(1) + 2 = 2(4) + 2 = 8 + 2 = 10
Now, you can find the third term by using the formula for the sequence:
f(3) = 2f(2) + 2 = 2(10) + 2 = 20 + 2 = 22
Therefore, the third term of the sequence is 22, not 16.
3) The explicit rule given is f(n) = (4 - n) / (n + 3). To find the third term, you substitute n = 3 into the equation:
f(3) = (4 - 3) / (3 + 3) = 1 / 6
So, your answer of 1/6 for the third term is correct.
4) The given sequence is 1, -2, -5, -8. To find the next four numbers and the function, observe the pattern between consecutive terms:
1 --> -2 (subtract 3)
-2 --> -5 (subtract 3)
-5 --> -8 (subtract 3)
From this pattern, it appears that each term is obtained by subtracting 3 from the previous term. Continuing this pattern:
-8 --> -11 (subtract 3)
-11 --> -14 (subtract 3)
So, the next four numbers in the sequence are -11, -14, -17, -20.
As for the function that generates this sequence, you can see that each term is obtained by starting with 1 and subtracting 3 times the position of the term. So, the function can be expressed as:
f(n) = 1 - 3n
Therefore, your answer for the next four numbers is correct, but the function is f(n) = 1 - 3n, not 4 - 3n.
I hope this helps clarify your work-checking! Let me know if you have any further questions.