Find the Sum of the Finite Geometric Sequence $$\sum _ { n = 1 } ^ { 6 } 2 \left( - \frac { 2 } { 3 } \right) ^ { n - 1 }$$

question 69

Multiple Choice

Find the sum of the finite geometric sequence.
$$\sum _ { n = 1 } ^ { 6 } 2 \left( - \frac { 2 } { 3 } \right) ^ { n - 1 }$$

• A) \(- \frac { 463 } { 243 }\)
• B) \(- \frac { 1024 } { 3 }\)
• C) 4256
• D) \(\frac { 55 } { 81 }\)
• E) \(\frac { 266 } { 243 }\)

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Definitions:

Projection Fibers

Nerve fibers that connect the cerebral cortex to other parts of the brain and to the spinal cord, facilitating communication between the brain and the rest of the body.

Cerebrum

The largest part of the brain, composed of the right and left hemispheres, responsible for complex brain functions such as thought and action.

Spinal Cord

A long, thin, tubular structure made up of nervous tissue, which extends from the brainstem down the back, housed within the spinal column.

Postcentral Gyrus

The region of the cerebral cortex located adjacent to the central sulcus, responsible for processing somatosensory information.