A(n) = 2 − 5(n − 1) what is the recursive formula
The given equation, or arithmetic sequence, is A(n) = 2 − 5(n − 1). To find the recursive formula, we need to express A(n) in terms of the previous term in the sequence.
Step 1: Determine the initial term of the sequence.
The given equation, A(n) = 2 − 5(n − 1), indicates that the initial term occurs when n = 1.
Substituting n = 1 into the equation, we get:
A(1) = 2 − 5(1 − 1)
A(1) = 2 − 5(0)
A(1) = 2 - 0
A(1) = 2
Therefore, the initial term of the sequence is A(1) = 2.
Step 2: Express A(n) in terms of A(n-1).
We can rewrite the given equation, A(n) = 2 − 5(n − 1), as follows:
A(n) = 2 - 5n + 5
Step 3: Rewrite the equation in terms of A(n-1).
To express A(n) in terms of A(n-1), we replace n with (n - 1) in the equation:
A(n) = 2 - 5(n - 1) + 5
A(n) = 2 - 5n + 5 + 5
A(n) = A(n - 1) - 5
Therefore, the recursive formula for the given arithmetic sequence is A(n) = A(n - 1) - 5.
To find the recursive formula for the given sequence, we first need to understand the given expression.
A(n) = 2 − 5(n − 1)
Here, A(n) represents the nth term of the sequence. The expression 2 - 5(n - 1) is used to calculate the value of each term.
To derive the recursive formula, we'll start by finding the first term in the sequence, A(1):
A(1) = 2 - 5(1 - 1)
= 2 - 5(0)
= 2 - 0
= 2
The first term is 2.
Now, let's find the second term, A(2):
A(2) = 2 - 5(2 - 1)
= 2 - 5(1)
= 2 - 5
= -3
The second term is -3.
To find the recursive formula, we observe that each term in the sequence is obtained by subtracting 5 from the previous term. Therefore, the recursive formula for the given sequence is:
A(n) = A(n-1) - 5
where A(n-1) represents the previous term in the sequence.
A(1) = 2
A(n+1) = 2-5(n+1-1) = 2 - 5n = 2-5(n-1) - 5 = A_n - 5