find the $6^{\text{th}}$ term of the geometric sequence represented below.

3. $1, 0.5, 0.25, \dots$

Question

find the $6^{\text{th}}$ term of the geometric sequence represented below.

3. $1, 0.5, 0.25, \dots$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Geometric Sequences", "Common Ratio", "Geometric Sequence Terms" ], "current_concepts": [ "Geometric Sequences", "Common Ratio", "Geometric Sequence Terms" ] } ## Identify sequence parameters $$ \begin{aligned} &a_1 = 1 \ &r = \frac{0.5}{1} = 0.5 \end{aligned} $$ ## Calculate the sixth term $$ \begin{aligned} &a_n = a_1 \cdot r^{n-1} \ &a_6 = 1 \cdot (0.5)^5 = 0.03125 \end{aligned} $$ Find the $6^{\text{th}}$ term of the geometric sequence represented below. 3. $1, 0.5, 0.25, \dots$ The $6^{\text{th}}$ term is $0.03125$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Geometric Sequence Terms" ] }

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Question

Explanation:

Identify sequence parameters

Calculate the sixth term

Answer: