what are the first three terms of a geometric sequence in which $a_5 = 25$ and the common ratio is 5?

* $\frac{1}{25}, \frac{1}{5}, 1$
* $25, 125, 625$
* $\frac{1}{25}, \frac{1}{125}, \frac{1}{625}$
* $125, 25, 5$

Question

what are the first three terms of a geometric sequence in which $a_5 = 25$ and the common ratio is 5?

* $\frac{1}{25}, \frac{1}{5}, 1$
* $25, 125, 625$
* $\frac{1}{25}, \frac{1}{125}, \frac{1}{625}$
* $125, 25, 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Geometric Sequences", "Common Ratio", "Geometric Sequence Explicit Formula" ], "new_concepts": [], "current_concepts": [ "Geometric Sequences", "Common Ratio", "Geometric Sequence Explicit Formula" ] } ## Identify the given values and formula Using the *Geometric Sequence Explicit Formula* and *Common Ratio* knowledge points $$ \begin{aligned} &a_5 = 25\ &r = 5\ &a_n = a_1 \cdot r^{n-1} \end{aligned} $$ ## Solve for the first term Using the *Geometric Sequence Explicit Formula* knowledge point $$ \begin{aligned} &25 = a_1 \cdot 5^{5-1}\ &25 = a_1 \cdot 5^4\ &25 = a_1 \cdot 625\ &a_1 = \frac{25}{625} = \frac{1}{25} \end{aligned} $$ ## Find the second and third terms Using the *Geometric Sequences* and *Common Ratio* knowledge points $$ \begin{aligned} &a_2 = a_1 \cdot r = \frac{1}{25} \cdot 5 = \frac{1}{5}\ &a_3 = a_2 \cdot r = \frac{1}{5} \cdot 5 = 1 \end{aligned} $$

(A) $\frac{1}{25}, \frac{1}{5}, 1$

(B) $25, 125, 625$

(C) $\frac{1}{25}, \frac{1}{125}, \frac{1}{625}$

(D) $125, 25, 5$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Geometric Sequences" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Solve for the first term

Find the second and third terms

Answer: