Find the 5th term of the geometric sequence where (a1=7)  and the common ratio  (r= 1/2)

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.

Learn how to find the 5th term of a geometric sequence where the first term (a_1) is 7 and the common ratio (r) is 1/2. Follow a detailed step-by-step solution using the geometric sequence nth term formula. Suitable for high school students.

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