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

question 27

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) \(\frac { 266 } { 243 }\)

Recognize the conditions under which a third party is bound by notifications given to an agent with apparent authority.

Distinguish between express and implied authority and their implications for principal-agent relationships.

Explain the concept of ratification and its types in agency relationships.

Understand the application of the doctrine of imputation in principal-agent relationships.

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Definitions:

Compounded Semi-annually

The process of adding interest to the principal sum of a deposit or loan every six months, so that each subsequent interest calculation is based on the original principal plus all accumulated interest.

Ordinary Annuity

A series of equal payments made at equal intervals of time, with the first payment occurring at the end of the period.

Present Value

The current value of a future sum of money or stream of cash flows given a specified rate of return.

Compounded Quarterly

The method of calculating interest where the interest is added to the principal sum four times a year.