Final answer:
The given sequence is arithmetic with a common difference of 8.7 and a first term of -9. The nᵗʰ term of the sequence can be found using the formula a₁ + (n - 1)d, which gives an = -9 + 8.7(n - 1).
Step-by-step explanation:
To determine the nᵗʰ term of the sequence -9, -0.300000000000001, 8.4, 17.1, 25.8, we first look for a pattern in the differences between terms. Calculating the differences between consecutive terms, we get:
- -0.300000000000001 - (-9) = 8.7
- 8.4 - (-0.300000000000001) = 8.7
- 17.1 - 8.4 = 8.7
- 25.8 - 17.1 = 8.7
We can see that the difference is consistent and equal to 8.7. This indicates that the sequence is arithmetic, with a common difference (d) of 8.7. The first term (a1) is -9. The formula for the nᵗʰ term of an arithmetic sequence is:
an = a1 + (n - 1)d
Substituting the known values, we get:
an = -9 + (n - 1)(8.7)
Therefore, the formula for the nᵗʰ term of the given sequence is an = -9 + 8.7(n - 1).