Find the Sum $$\frac { 1 } { 7 } + \frac { 3 } { 7 } + \frac { 3 ^ { 2 } } { 7 } + \frac { 3 ^ { 3 } } { 7 } + \cdots + \frac { 3 ^ { n - 1 } } { 7 }$$

question 97

Multiple Choice

Find the sum.
- $$\frac { 1 } { 7 } + \frac { 3 } { 7 } + \frac { 3 ^ { 2 } } { 7 } + \frac { 3 ^ { 3 } } { 7 } + \cdots + \frac { 3 ^ { n - 1 } } { 7 }$$

• A) \(- \frac { 1 } { 7 } \left( 1 - 3 ^ { n } \right)\)
• B) \(\frac { 1 } { 14 } \left( 1 - 3 ^ { n } \right)\)
• C) \(- \frac { 2 } { 7 } \left( 1 - 3 ^ { n } \right)\)
• D) \(- \frac { 1 } { 14 } \left( 1 - 3 ^ { n } \right)\)

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Definitions:

Postural Muscles

Muscles that are primarily responsible for stabilizing the body and maintaining posture.

Breathing Rate

The number of breaths taken per minute, which can vary based on factors such as physical activity, emotional state, and overall health.

Heart Rate

The number of heartbeats per unit of time, typically expressed in beats per minute (bpm), indicating the heart's efficiency in circulating blood throughout the body.

Brain Activity

The electrical and metabolic phenomena occurring within the brain that are associated with functional operations and processes.