Final answer:
The sequence is an arithmetic sequence with a common difference of -4.6. The formula for the nth term (an) is an = 10 + (n - 1)(-4.6), where n is the position of the term in the sequence.
Step-by-step explanation:
The student is asking to find the nᵗʰ term of the sequence 10, 5.4, 0.8 (approximating 0.799999999999999), -3.8, -8.4. To derive a formula for the nth term, let's analyze the differences between the terms. We notice that each term is obtained by subtracting a fixed number from the preceding term.
Here is the step-by-step process for finding the difference:
- The difference between the first and second terms: 5.4 - 10 = -4.6
- The difference between the second and third terms: 0.8 (approx) - 5.4 = -4.6
- Similarly, the difference between the remaining terms is also -4.6.
Thus, we see that the sequence is an arithmetic sequence with a common difference of -4.6. The formula for the nth term 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.
Using the first term (a1 = 10) and the common difference (d = -4.6), the formula for the nth term of this sequence is:
an = 10 + (n - 1)(-4.6)