write a rescursive formula for an, the nth term of the sequence 1,-6,-13,-20
To find a recursive formula for the sequence 1, -6, -13, -20, we need to determine the relationship between each term and its previous term.
Looking at the sequence, we can observe that each term is 7 less than the previous term:
1 → -6 → -13 → -20
Therefore, the recursive formula for this sequence is:
an = an-1 - 7
where an represents the nth term of the sequence.
To find a recursive formula for the sequence 1, -6, -13, -20, we can look for a pattern in the differences between consecutive terms.
First, let's observe the differences:
-6 - 1 = -7
-13 - (-6) = -7
-20 - (-13) = -7
We can see that the difference between consecutive terms is always -7. This means that to get the next term, we subtract 7 from the previous term.
Now, let's denote the previous term as a sub-n, and the next term as a sub-(n+1). The recursive formula can be written as:
a sub-(n+1) = a sub-n - 7
Using this formula, we can find any term in the sequence by starting with the initial term, which is given as a sub-1 = 1, and applying the recursive formula repeatedly.