Final answer:
The general term for the alternating sequence 6, -4, 6, -4, ... can be expressed as an = 5(-1)n + 1.
Step-by-step explanation:
The given sequence alternates between 6 and -4, which suggests that the formula for the general term an will involve (-1)n to account for the alternating sign. One way to establish a pattern for a sequence that alternates in this way is to use power of (-1) raised to some function of n. The general term an can be expressed as:
an = 5(-1)n + 1
This formula accounts for the alternating pattern: when n is odd, (-1)n is -1, giving us 5(-1)+1, which equals -4; and when n is even, (-1)n equals 1, giving us 5(1)+1, which equals 6. Thus, this formula correctly generates the terms of the sequence.