Final answer:
The nth term of the sequence 13, 8.8, 4.6, 0.4, -3.8 is given by the formula an= 17.2 - 4.2n, derived using the first term and the common difference of the linear progression.
Step-by-step explanation:
To determine the nth term of the sequence 13, 8.8, 4.6, 0.4, -3.8, we first need to identify the pattern of the sequence. By looking at the differences between the terms, we see that the difference changes by -4.2 each time (13 - 8.8 = 4.2, 8.8 - 4.6 = 4.2, etc.). As this is a linear pattern, we can use the common difference to find the nth term.
The first term a1 is 13 and the common difference d is -4.2. The nth term of a linear sequence is given by an = a1 + (n-1)*d. Substituting the values into the formula gives us:
an = 13 + (n-1)*(-4.2)
= 13 - 4.2n + 4.2
= 17.2 - 4.2n
Therefore, the nth term of the sequence is given by an= 17.2 - 4.2n.