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91Ó°ÊÓ

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=6, r=\frac{1}{2}\).

Short Answer

Expert verified
The eighth term, \(a_{8}\), of the given geometric sequence is \(\frac{3}{32}\).

Step by step solution

01

Understanding the formula for the nth term of a geometric sequence

The formula for the nth term of a geometric sequence is \(a_{n} = a_{1} \cdot r^{(n-1)}\). Here, \(a_{1}\) stands for the first term, \(r\) for the common ratio, and \(n\) for the term number.
02

Substituting the values in the equation

The exercise gives us \(a_{1}=6\), \(r=\frac{1}{2}\), and asks for \(a_{8}\). Substituting these values into our equation, \(a_{8} = a_{1} \cdot r^{(8-1)} = 6 \cdot \left(\frac{1}{2}\right)^7\)
03

Calculate the value of \(a_{8}\)

After performing the calculation, the result is \(a_{8} = \frac{3}{32}\).

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