To find the 5th term of a geometric sequence, you can use the formula:

$a_n = a_1 \times r^{(n-1)}$

Where:

• $a_n$ is the nth term.
• $a_1$ is the first term.
• $r$ is the common ratio.
• $n$ is the term number.

Given:

• $a_1 = 7$
• $r = \frac{1}{2}$
• $n = 5$

Now, substitute these values into the formula:

$a_5 = 7 \times \left(\frac{1}{2}\right)^{(5-1)} = 7 \times \left(\frac{1}{2}\right)^4$

Calculate $\left(\frac{1}{2}\right)^4$:

$\left(\frac{1}{2}\right)^4 = \frac{1}{16}$

Now, multiply by 7:

$a_5 = 7 \times \frac{1}{16} = \frac{7}{16}$

So, the 5th term of the sequence is $\frac{7}{16}$.

Would you like more details or have any questions?

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Here are five related questions:

1. How do you find the sum of the first 5 terms in this geometric sequence?
2. What would be the 8th term in this sequence?
3. If the common ratio were $\frac{1}{3}$ instead, what would the 5th term be?
4. How does the common ratio affect the sequence as $n$ increases?
5. Can you determine the 5th term if the first term and the common ratio were unknown but two other terms were provided?

Tip: When dealing with geometric sequences, always ensure the common ratio is correctly applied, especially with fractions or negative numbers.