Final answer:
To find the n-th term of the given arithmetic sequence, apply the formula a_n = a_1 + (n - 1)d, resulting in the n-th term being 1.96 plus 0.04 times n.
Step-by-step explanation:
The student has asked to determine the nth term of the sequence 2, 2.04, 2.08, 2.12, 2.16. This is an arithmetic sequence where the common difference between the terms is 0.04.
To find the nth term of an arithmetic sequence, the formula to use is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
The given sequence starts with 2 and increases by 0.04 with each term. We can observe that the difference between consecutive terms is constant. Therefore, this is an arithmetic sequence with a common difference of 0.04.
For this sequence, a1 = 2 and d = 0.04. Using the formula, we get:
an = 2 + (n - 1) × 0.04
an = 2 + 0.04n - 0.04
an = 1.96 + 0.04n
Therefore, the nth term of the sequence is 1.96 plus 0.04 times n.