4. For the following sequence, give an explicit formula for the $$ n $$th term for $$ n \geq 2 $$. $$ a_{1}=2, a_{n+1}=\frac{a_{n}}{2} $$ 4.

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We are given the sequence defined by
$$
a_{1} = 2 \quad \text{and} \quad a_{n+1} = \frac{a_{n}}{2}.
$$

1. Notice that at each step, the term is multiplied by $$\frac{1}{2}$$. This is a geometric sequence with common ratio $$r = \frac{1}{2}$$.

2. The general form of a geometric sequence is
$$
a_{n} = a_{1} \cdot r^{n-1}.
$$

3. Substituting the given values, we obtain
$$
a_{n} = 2 \cdot \left(\frac{1}{2}\right)^{n-1}.
$$

Thus, the explicit formula for the $$n$$th term of the sequence is
$$
\boxed{a_{n} = 2 \cdot \left(\frac{1}{2}\right)^{n-1}}.
$$
The $$n$$th term of the sequence is $$a_{n} = 2 \cdot \left(\frac{1}{2}\right)^{n-1}$$.

For the following sequence, give an explicit formula for the th term for .

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