Final answer:
To find the nᵗʰ term of the arithmetic sequence -3, -12.7, -22.4, -32.1, -41.8, we first calculate the common difference which is -9.7.
Step-by-step explanation:
To determine the nᵗʰ term of the given sequence -3, -12.7, -22.4, -32.1, -41.8, we must first identify the pattern. The sequence is arithmetic as there is a common difference between consecutive terms.Then we use the formula for the nᵗʰ term of an arithmetic sequence, resulting in the nᵗʰ term being -9.7n + 6.7.
Let's calculate the common difference:
-12.7 - (-3) = -9.7
-22.4 - (-12.7) = -9.7
-32.1 - (-22.4) = -9.7
-41.8 - (-32.1) = -9.7
Since the common difference is -9.7, we can express the nᵗʰ term as:
an = a1 + (n - 1)d
where a1 is the first term and d is the common difference.
So, substituting the values:
an = -3 + (n - 1)(-9.7) = -3 - 9.7n + 9.7 = -9.7n + 6.7
Therefore, the nᵗʰ term of the sequence is -9.7n + 6.7.