Final answer:
The nᵗʰ term of the sequence 8, 7.93, 7.86, 7.79, 7.72 is given by the formula 8.07 - 0.07n, which reflects that the sequence decreases by 0.07 with each term.
Step-by-step explanation:
To determine the nth term of a given sequence 8, 7.93, 7.86, 7.79, 7.72, we first have to identify the pattern or the rule that the sequence follows. By examining the differences between terms, we can see that each term decreases by 0.07 from the previous term. Therefore, this is an arithmetic sequence.
The general form of an arithmetic sequence is given by:
An = A1 + (n - 1)d
where:
An is the nth term,
A1 is the first term, and
d is the common difference between the terms.
For the given sequence:
- A1 = 8 (the first term),
- d = -0.07 (the common difference).
Substituting these values into the general form yields the nth term of the sequence:
An = 8 + (n - 1)(-0.07)
An = 8 - 0.07n + 0.07
An = 8.07 - 0.07n
So, the nth term of the sequence is 8.07 - 0.07n.