Question
Multiple Choice 10 points Find the 7 th term in the sequence \( a_{n}=\frac{1}{2}(3)^{n-1} \) 364.5 1093.5 17.1 1458
Ask by Guzman Mullins. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The 7th term is 364.5.
Solution
To find the 7th term, substitute n = 7 into the formula:
a₇ = (1/2) × 3^(7–1)
= (1/2) × 3⁶
= (1/2) × 729
= 364.5
Thus, the correct answer is 364.5.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To find the 7th term in the sequence \( a_{n}=\frac{1}{2}(3)^{n-1} \), we can plug in \( n = 7 \): \[ a_{7} = \frac{1}{2}(3)^{7-1} = \frac{1}{2}(3)^{6} \] Calculating \( (3)^{6} = 729 \), we get: \[ a_{7} = \frac{1}{2} \times 729 = 364.5 \] So, the 7th term is **364.5**!
