a sequence is defined by the following:

\a_n = 4^{n-1}\

what is $a_1$?

what is $a_8$?

Question

a sequence is defined by the following:

\a_n = 4^{n-1}\

what is $a_1$?

what is $a_8$?

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Sequence Notation", "Exponent Rules" ], "new_concepts": [ "Explicit Sequence Evaluation" ], "current_concepts": [ "Sequence Notation", "Exponent Rules", "Explicit Sequence Evaluation" ] } ## Evaluate the first term of the sequence Using the *Sequence Notation* knowledge point $$ \begin{aligned} a_n &= 4^{n-1} \ a_1 &= 4^{1-1} \ a_1 &= 4^0 \end{aligned} $$ ## Simplify the exponent for the first term Using the *Exponent Rules* knowledge point $$ a_1 = 1 $$ ## Evaluate the eighth term of the sequence Using the *Sequence Notation* knowledge point $$ \begin{aligned} a_8 &= 4^{8-1} \ a_8 &= 4^7 \end{aligned} $$ ## Calculate the value of the eighth term Using the *Exponent Rules* knowledge point $$ \begin{aligned} 4^7 &= (2^2)^7 = 2^{14} \ 4^7 &= 16384 \end{aligned} $$ ## Question 1 The value of $a_1$ is 1. ## Question 2 The value of $a_8$ is 16384. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Sequence Notation" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the first term of the sequence

Simplify the exponent for the first term

Evaluate the eighth term of the sequence

Calculate the value of the eighth term

Answer:

Question 1

Question 2