a sequence is defined recursively by the formula $f(n + 1) = -2f(n)$. the first term of the sequence is $-1.5$. what is the next term in the sequence?

$\bigcirc$ $-3.5$
$\bigcirc$ $-3$
$\bigcirc$ $0.5$
$\bigcirc$ $3$

Question

a sequence is defined recursively by the formula $f(n + 1) = -2f(n)$. the first term of the sequence is $-1.5$. what is the next term in the sequence?

$\bigcirc$ $-3.5$
$\bigcirc$ $-3$
$\bigcirc$ $0.5$
$\bigcirc$ $3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Sequences", "Recursive Formulas" ], "new_concepts": [], "current_concepts": [ "Geometric Sequences", "Recursive Formulas" ] } ## Identify the given values and recursive formula $$ \begin{aligned} f(1) &= -1.5 \ f(n+1) &= -2f(n) \end{aligned} $$ ## Calculate the next term in the sequence $$ \begin{aligned} f(2) &= -2f(1) \ f(2) &= -2(-1.5) \ f(2) &= 3 \end{aligned} $$

-3.5

-3

0.5

3

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Recursive Formulas" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given values and recursive formula

Calculate the next term in the sequence

Answer: