Find a Formula for the Sum of the N Terms $\frac { 1 } { 5 } , \frac { 3 } { 25 } , \frac { 9 } { 125 } , \frac { 27 } { 625 } , \mathbf { K }$

question 80

Multiple Choice

Find a formula for the sum of the n terms of the sequence. $\frac { 1 } { 5 } , \frac { 3 } { 25 } , \frac { 9 } { 125 } , \frac { 27 } { 625 } , \mathbf { K }$

• A) \(- \frac { 3 ^ { n } - 5 ^ { n } } { 2 \left( 5 ^ { n } \right) }\)
• B) \(- \frac { 3 \left( 3 ^ { n } - 5 ^ { n } \right) } { 2 \left( 5 ^ { n } \right) }\)
• C) \(\frac { 3 ^ { n - 1 } } { 5 ^ { n } }\)
• D) \(\frac { 3 ^ { n } + 5 ^ { n } } { 8 ( 5 ) ^ { n } }\)
• E) \(\frac { 1 } { 5 ^ { n } }\)

---

Definitions:

Europeans

People native to or residing within the continent of Europe, often relating to the cultural, social, and political characteristics of this diverse region.

Prototype

A mental image or best example of a category. Matching new items to a prototype provides a quick and easy method for sorting items into categories (as when comparing feathered creatures to a prototypical bird, such as a robin).

Mental Grouping

The cognitive process of organizing concepts, objects, or ideas into categories based on common properties to simplify understanding and memory.

Step-by-Step

Involves breaking down information, processes, or problems into smaller, manageable parts to facilitate understanding or completion.