Find a_(3).
a_(1)=28
a_(n)=(1)/(2)a_(n-1)
Write your answer as an integer or fraction in simplest form.
a_(3)=

Submit

We are given the recursive sequence formula:

\[
a_1 = 28
\]
\[
a_n = \frac{1}{2} a_{n-1}
\]

We need to find \( a_3 \).

### Step 1: Find \( a_2 \)

Using the recursive formula with \( n = 2 \):

\[
a_2 = \frac{1}{2} a_1 = \frac{1}{2} \times 28 = 14
\]

### Step 2: Find \( a_3 \)

Now, using the recursive formula with \( n = 3 \):

\[
a_3 = \frac{1}{2} a_2 = \frac{1}{2} \times 14 = 7
\]

So, the value of \( a_3 \) is:

\[
a_3 = 7
\]

Would you like any further explanation?

### Related Questions:
1. What would \( a_4 \) be in this sequence?
2. Can you express \( a_n \) explicitly as a function of \( n \)?
3. How does this recursive formula compare to geometric sequences?
4. What happens if the initial term \( a_1 \) was different, say \( a_1 = 32 \)?
5. Can this sequence reach zero at any value of \( n \)?

**Tip:** Recursive formulas require the value of previous terms, so it's helpful to compute terms sequentially.

Find a_(3). a_(1)=28 a_(n)=(1)/(2)a_(n-1) Write your answer as an integer or fraction in simplest form. a_(3)=

Learn how to solve the recursive sequence problem to find a_3 when a_1 = 28 and a_n = (1/2) * a_(n-1). This step-by-step solution demonstrates how to apply the recursive formula to calculate terms sequentially, suitable for students in Grades 7-9.

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