Find the Fifth Term and the Nth Term of the Geometric

question 22

Multiple Choice

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
- $$\mathrm { a } = 5 ; \mathrm { r } = 3 \pi$$

• A) \(a _ { 5 } = 405 \pi , a _ { n } = 5 \cdot 3 ^ { n - 1 } \pi\)
• B) \(a _ { 5 } = 1,215 \pi ^ { 5 } , a _ { n } = 5 \cdot 3 ^ { n } \pi ^ { n }\)
• C) \(a _ { 5 } = 5 + 12 \pi , a _ { n } = 5 + 3 \pi ( n - 1 )\)
• D) a5 \(= 405 \pi ^ { 4 } , a _ { n } = 5 \cdot 3 ^ { n - 1 } \pi ^ { n - 1 }\)

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Definitions:

Quartz-Rich

Containing a high concentration of quartz, a hard, crystalline mineral composed of silicon and oxygen atoms.

Soluble Chemical

A substance capable of being dissolved in a solvent, particularly water, to form a solution.

Poor Solubility

Describes a substance's low capability to dissolve in a solvent, typically referring to solids in liquids.

Quartz

A hard, crystalline mineral composed of silicon and oxygen atoms, common in the Earth's crust and used in various applications due to its durability and piezoelectric properties.