**Geometric Sequences: Finding the 7th Term****Problem:**Find the 7th term of the geometric sequence whose common ratio is \(\frac{3}{2}\) and whose first term is 4.**Solution:**To find the nth term of a geometric sequence, use the formula:\[ a_n = a_1 \cdot r^{(n-1)} \]where:- \( a_n \) is the nth term- \( a_1 \) is the first term- \( r \) is the common ratio- \( n \) is the term numberGiven data:- First term (\( a_1 \)) = 4- Common ratio (r) = \(\frac{3}{2}\)- Term number (n) = 7Step-by-step calculation:1. Substitute the given values into the formula:\[ a_7 = 4 \cdot \left(\frac{3}{2}\right)^{(7-1)} \]2. Calculate \( \left(\frac{3}{2}\right)^{6} \):\[ \left(\frac{3}{2}\right)^6 = \frac{3^6}{2^6} = \frac{729}{64} \]3. Multiply by the first term:\[ a_7 = 4 \cdot \frac{729}{64}\]4. Simplify the multiplication:\[ a_7 = \frac{4 \cdot 729}{64} = \frac{2916}{64} \]5. Simplify the fraction:\[ a_7 = 45.5625 \]Therefore, the 7th term of the geometric sequence is 45.5625.---This problem also contains a user input box for submitting answers and symbols for actions such as clearing the fields (X), resetting (circular arrow), and help (question mark) commonly found in educational software interfaces.

Name: **Geometric Sequences: Finding the 7th Term****Problem:**Find the 7th
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: **Geometric Sequences: Finding the 7th Term****Problem:**Find the 7th term of the geometric sequence whose common ratio is \(\frac{3}{2}\) and whose first term is 4.**Solution:**To find the nth term of a geometric sequence, use the formula:\[ a_n =