what is the explicit rule for the sequence 10.5,9,7.5,6.4.5
The explicit rule for the sequence 10.5, 9, 7.5, 6.4, 5 is that each term is obtained by subtracting 1.5 from the previous term.
To find the explicit rule for a sequence, we need to try to identify a pattern in the sequence.
Looking at the given sequence, we can observe that each term is obtained by subtracting a certain constant value from the previous term.
First, let’s find the common difference between consecutive terms:
9 - 10.5 = -1.5
7.5 - 9 = -1.5
6 - 7.5 = -1.5
We can see that the difference between consecutive terms is consistently -1.5.
So, we can establish that the explicit rule for this sequence is to subtract 1.5 from the previous term to get the next term.
Therefore, the explicit rule for the sequence 10.5, 9, 7.5, 6 is:
T(n) = T(n-1) - 1.5
To find the explicit rule for the given sequence, we need to look for a pattern or formula that generates each term.
Looking at the sequence: 10.5, 9, 7.5, 6, 4.5
We can observe that each term is decreasing by 1.5.
Therefore, the explicit rule for the given sequence is:
nth term = 10.5 - (n-1) * 1.5
where n is the position of the term in the sequence.