Final answer:
The nth term of the sequence -1, -1.1, -1.2, -1.3, -1.4 is given by the formula an = -1.1 + 0.1n.
Step-by-step explanation:
The question requires us to find the nth term of the given sequence -1, -1.1, -1.2, -1.3, -1.4. Observing that each term is reduced by 0.1 from the previous term, we can derive the nth term. The first term (a1) is -1, and the common difference (d) is -0.1 in this arithmetic sequence. The nth term of an arithmetic sequence is given by the formula an = a1 + (n - 1) * d. Using this formula, the nth term for this sequence would be: an = -1 + (n - 1) * (-0.1).
The given sequence -1, -1.1, -1.2, -1.3, -1.4 follows a pattern where each term is obtained by subtracting 0.1 from the previous term. So, the common difference between the terms is -0.1.
To find the nᵗʰ term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. In this case, a1 = -1 and d = -0.1.
Using the formula, the nth term of the given sequence is: an = -1 + (n-1)(-0.1)
Simplifying, we get: an = -1 - 0.1n + 0.1, which further simplifies to an = -1.1 + 0.1n. Therefore, the nth term of the sequence is an = -1.1 + 0.1n.