find the first six terms of the sequence, starting with $n = 1$.

\a_1 = 1, a_2 = 1, \text{ and } a_{n + 2} = a_n + a_{n + 1} \text{ for } n \ge 1\

$a_1 = $
$a_2 = $
$a_3 = $
$a_4 = $
$a_5 = $
$a_6 = $

Question

find the first six terms of the sequence, starting with $n = 1$.

\a_1 = 1, a_2 = 1, \text{ and } a_{n + 2} = a_n + a_{n + 1} \text{ for } n \ge 1\

$a_1 = $
$a_2 = $
$a_3 = $
$a_4 = $
$a_5 = $
$a_6 = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Recursive Formulas", "Sequence Terms" ], "new_concepts": [], "current_concepts": [ "Recursive Formulas", "Sequence Terms", "Fibonacci Sequence" ] } ## Identify the given initial terms and recurrence relation $$ \begin{aligned} a_1 &= 1 \ a_2 &= 1 \ a_{n+2} &= a_n + a_{n+1}, \quad n \ge 1 \end{aligned} $$ ## Calculate the terms from n = 1 to n = 4 $$ \begin{aligned} a_3 &= a_1 + a_2 = 1 + 1 = 2 \ a_4 &= a_2 + a_3 = 1 + 2 = 3 \ a_5 &= a_3 + a_4 = 2 + 3 = 5 \ a_6 &= a_4 + a_5 = 3 + 5 = 8 \end{aligned} $$ Find the first six terms of the sequence, starting with $n = 1$. $a_1 = 1, a_2 = 1$, and $a_{n+2} = a_n + a_{n+1}$ for $n \ge 1$ $a_1 =$ 1 $a_2 =$ 1 $a_3 =$ 2 $a_4 =$ 3 $a_5 =$ 5 $a_6 =$ 8 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Recursive Formulas" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given initial terms and recurrence relation

Calculate the terms from n = 1 to n = 4

Answer: