Write a Formula for the General Term (The Nth Term) $$- \frac { 1 } { 3 } , \frac { 1 } { 24 } , - \frac { 1 } { 192 } , \frac { 1 } { 1536 } , \ldots$$

question 107

Multiple Choice

Write a formula for the general term (the nth term) of the geometric sequence.
- $$- \frac { 1 } { 3 } , \frac { 1 } { 24 } , - \frac { 1 } { 192 } , \frac { 1 } { 1536 } , \ldots$$

• A) \(a _ { n } = - \frac { 1 } { 3 } \left( - \frac { 1 } { 8 } \right) ^ { n }\)
• B) \(a _ { n } = - \frac { 1 } { 3 } - \frac { 1 } { 8 } ( n - 1 )\)
• C) \(a _ { n } = - \frac { 1 } { 8 } \left( - \frac { 1 } { 3 } \right) ^{n - 1}\)
• D) \(a _ { n } = \left( - \frac { 1 } { 3 } \right) ^ { n - 1 } + \frac { 3 } { 8 }\)

---

Definitions:

Years From Now

A future point in time referenced from the present moment, often used in planning and projections.

Interest Rate

The fraction of a loan incurred as interest cost to the borrower, often expressed annually as a percentage of the total loan amount still due.

Interest Rate

The cost of borrowing money or the reward for saving, usually expressed as a percentage of the principal amount per annum.

Years From Now

This term projects a future timeline or point in time from the present moment.