A = - 113 and A = -213
20 40
this is an arithmetic sequence
and i have to find the explicit formula and the recursive formula
how do i do that?
To find the explicit formula and the recursive formula for the given arithmetic sequence, we can start by examining the pattern in the sequence.
In an arithmetic sequence, each term is obtained by adding a constant difference, called the common difference, to the previous term. In this case, it seems that the common difference is -20.
To find the explicit formula for an arithmetic sequence, we can use the following formula:
Term(n) = Term(1) + (n - 1) * Common Difference
where Term(n) represents the value of the nth term in the sequence, Term(1) represents the value of the first term, n represents the position of the term in the sequence, and the Common Difference represents the constant difference between each term.
Let's calculate the explicit formula:
For the first term (n = 1):
Term(1) = -113
Using the formula, we have:
Term(n) = -113 + (n - 1) * (-20)
Therefore, the explicit formula for this arithmetic sequence is:
Term(n) = -113 - 20n + 20
To find the recursive formula for an arithmetic sequence, we need to express each term in terms of the previous term. In this case, we can observe the following pattern:
Term(1) = -113
Term(2) = -113 - 20
Term(3) = -113 - 2 * 20
Term(4) = -113 - 3 * 20
...
We can see that each term can be obtained by subtracting the common difference (-20) from the previous term.
Using this pattern, we can define the recursive formula for this arithmetic sequence:
Term(1) = -113
Term(n) = Term(n-1) - 20
So, the recursive formula for this arithmetic sequence is:
Term(n) = Term(n-1) - 20 with the initial term, Term(1) = -113.
Now you have the explicit formula and the recursive formula for the given arithmetic sequence.