Final answer:
The nth term of the arithmetic sequence -7, -6.1, -5.2, -4.3, -3.4 is 0.9n - 7.9, determined using the formula for an arithmetic sequence's nth term.
Step-by-step explanation:
The student wants to determine the nth term of the sequence -7, -6.1, -5.2, -4.3, -3.4. To find the nth term, we first identify the pattern in the sequence. Noticing that each term increases by 0.9, we can say that the sequence has a common difference of +0.9. Therefore, the given sequence is an arithmetic sequence.
To determine the nth term formula for an arithmetic sequence, the formula is:
a_n = a_1 + (n - 1)d
Where:
- a_n is the nth term
- a_1 is the first term in the sequence, which is -7
- n is the term number
- d is the common difference between the terms, which is +0.9
Using this formula, the nth term of the sequence can be calculated as:
a_n = -7 + (n - 1)(0.9)
a_n = -7 + 0.9n - 0.9
By simplifying, we get:
a_n = 0.9n - 7.9
Therefore, the nth term of the sequence is 0.9n - 7.9.