2. The function A(n) = 5 + (n-1) (4) represents an arithmetic sequence. Which of the following formulas represents the same sequence? Select all that apply
I got
a1=5
an=an-1+4
And
an=5+4(n-1)
whats your answer
what the answer you should know beacuse i take you 4 year. please i need this
These are the answers for
Formulas for Arithmetic Sequences
D
A,F
B
Oh, arithmetic sequences! Those are like the "mathematical jokers" of the sequence world. Let's see if we can find a formula that laughs along with the given sequence.
The formula A(n) = 5 + (n-1)(4) can be simplified a bit by distributing the 4:
A(n) = 5 + 4n - 4
That gives us:
A(n) = 1 + 4n
Now, we need to find formulas that will keep this sequence chuckling. Here are a few contenders:
1. B(n) = 2 + 4n: This one is the result of adding 1 to our original formula. Adding 1 isn't enough to tickle the sequence, so this formula doesn't represent the same sequence.
2. C(n) = 1 + 5n: Ah, this one has the 4 disguised as 5. The sequence won't fall for that trick! So, this formula doesn't represent the same sequence either.
3. D(n) = 5n + 1: Hold on, we may have a winner here! This formula has the 4 in its correct place with the coefficient n. Looks like this formula shares the same sense of humor as the original sequence.
So, the formula D(n) = 5n + 1 represents the same arithmetic sequence as A(n) = 5 + (n-1)(4).
Remember, laughter is always the best formula!
To determine which formulas represent the same arithmetic sequence as the given function, we need to understand the general formula for arithmetic sequences.
An arithmetic sequence follows a pattern where each term is obtained by adding a constant difference (d) to the previous term. The general formula for an arithmetic sequence can be written as:
A(n) = a + (n-1)d
where A(n) represents the nth term of the sequence, a represents the first term, n represents the position of the term in the sequence, and d represents the common difference.
Comparing the given function A(n) = 5 + (n-1)(4) with the general formula, we can identify that the first term (a) is 5, and the common difference (d) is 4.
Now, let's analyze the options to see which ones match the given arithmetic sequence formula (A(n) = a + (n-1)d).
Option 1: A(n) = 5n + 4
Comparing this option with the general formula, we can observe that the constant term in the general formula is missing here. Therefore, this option does not represent the same arithmetic sequence.
Option 2: A(n) = 4n + 1
Comparing this option with the general formula, we can observe that the constant term in the general formula is missing here. Therefore, this option does not represent the same arithmetic sequence.
Option 3: A(n) = 4n + 5
Comparing this option with the general formula, we can see that it matches; the first term (a) is 5, and the common difference (d) is 4.
Therefore, the formulas that represent the same arithmetic sequence as the given function are:
- A(n) = 5 + (n-1)(4)
- A(n) = 4n + 5
In conclusion, option 1 (A(n) = 5n + 4) and option 2 (A(n) = 4n + 1) do not represent the same arithmetic sequence, while option 3 (A(n) = 4n + 5) does.