Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 3 + + 16 3 + 64 15 Converges; 4 Converges; 4 Converges; O Diverges
Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 3 + + 16 3 + 64 15 Converges; 4 Converges; 4 Converges; O Diverges
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**QUESTION 1**
Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
\[ 3 + \frac{3}{4} + \frac{3}{16} + \frac{3}{64} + \ldots \]
- ☐ Converges; \(\frac{15}{4}\)
- ☐ Converges; 4
- ☐ Converges; \(\frac{3}{4}\)
- ☐ Diverges
---
**QUESTION 2**
Find the fifth term and the \(n\)th term of the geometric sequence whose initial term, \(a\), and common ratio, \(r\), are given.
\[ a = 3; \quad r = 5 \]
- ☐ \(a_5 = 9375;\ a_n = 3 \cdot (5)^{n-1}\)
- ☐ \(a_5 = 9375;\ a_n = 3 \cdot (5)^{n}\)
- ☐ \(a_5 = 1875;\ a_n = 3 \cdot (5)^{n}\)
- ☐ \(a_5 = 1875;\ a_n = 3 \cdot (5)^{n-1}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26f0e1f3-8f59-40a4-87b0-28483e544017%2F35b7d4e5-7581-4830-8ecf-759bb5831b99%2F0h242j_processed.png&w=3840&q=75)
Transcribed Image Text:**QUESTION 1**
Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
\[ 3 + \frac{3}{4} + \frac{3}{16} + \frac{3}{64} + \ldots \]
- ☐ Converges; \(\frac{15}{4}\)
- ☐ Converges; 4
- ☐ Converges; \(\frac{3}{4}\)
- ☐ Diverges
---
**QUESTION 2**
Find the fifth term and the \(n\)th term of the geometric sequence whose initial term, \(a\), and common ratio, \(r\), are given.
\[ a = 3; \quad r = 5 \]
- ☐ \(a_5 = 9375;\ a_n = 3 \cdot (5)^{n-1}\)
- ☐ \(a_5 = 9375;\ a_n = 3 \cdot (5)^{n}\)
- ☐ \(a_5 = 1875;\ a_n = 3 \cdot (5)^{n}\)
- ☐ \(a_5 = 1875;\ a_n = 3 \cdot (5)^{n-1}\)
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