Final answer:
The nth term of the sequence 2, -4.4, -10.8, -17.2, -23.6 is An = -6.4n + 8.4, which is found by identifying the common difference and applying the arithmetic series formula.
Step-by-step explanation:
To find the nth term of the given sequence 2, -4.4, -10.8, -17.2, -23.6, we must determine the pattern by which the terms are changing. We can observe that each term decreases by -6.4 from the previous term. This is a linear sequence, and we can write the nth term as an arithmetic sequence formula:
An = a + (n - 1)d
where,
- An is the nth term of the sequence,
- a is the first term of the sequence,
- d is the common difference between the terms, and
- n is the term number.
In our case, the first term (a) is 2, and the common difference (d) is -6.4. Plugging these values into the formula gives:
An = 2 + (n - 1)(-6.4)
An = 2 - 6.4n + 6.4
An = -6.4n + 8.4
So, the nth term of the sequence is An = -6.4n + 8.4.