Final answer:
The n^th term of the sequence -10, -10.05, -10.1, -10.15, -10.2 is given by the formula a_n = -10.05 + 0.05n, where a_n represents the n^th term and n is the position of the term in the sequence.
Step-by-step explanation:
To find the nth term of the sequence -10, -10.05, -10.1, -10.15, -10.2, we first observe that the difference between each term is -0.05. This indicates that the sequence is an arithmetic sequence, which means its nth term can be found using the formula:
an = a1 + (n - 1) * d
where a1 is the first term and d is the common difference between the terms. In this sequence, a1 = -10 and d = -0.05.
Substituting these values into the formula, we get:
an = -10 + (n - 1) * (-0.05)
This simplifies to:
an = -10 - 0.05n + 0.05
And then simplifies further to:
an = -10.05 + 0.05n
This expression represents the n terms of the sequence.