consider the sequence:
6, 10, 14, 18, 22, ...

for this sequence, what is $a_3$?
$a_3 = 14$

which of the following describes the pattern in terms of the sequence?
add 4 to the previous term to get the next term.

what is the explicit formula of the sequence?
$a_n = 2 + 2n$
$a_n = 4 + 4n$
$a_n = 2 + 4n$
$a_n = 4 - 4n$

Question

consider the sequence:
6, 10, 14, 18, 22, ...

for this sequence, what is $a_3$?
$a_3 = 14$

which of the following describes the pattern in terms of the sequence?
add 4 to the previous term to get the next term.

what is the explicit formula of the sequence?
$a_n = 2 + 2n$
$a_n = 4 + 4n$
$a_n = 2 + 4n$
$a_n = 4 - 4n$

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": [ "Arithmetic Sequences" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Sequence Notation" ] } ## Identify the sequence type and parameters Using the *Arithmetic Sequences* knowledge point $$ \begin{aligned} &\text{Sequence: } 6, 10, 14, 18, 22, \dots\ &a_1 = 6\ &d = 10 - 6 = 4 \end{aligned} $$ ## Determine the explicit formula Using the *Arithmetic Sequences* knowledge point $$ \begin{aligned} &a_n = a_1 + (n - 1)d\ &a_n = 6 + (n - 1)4\ &a_n = 6 + 4n - 4\ &a_n = 2 + 4n \end{aligned} $$

(A) $a_n = 2 + 2n$

(B) $a_n = 4 + 4n$

(C) $a_n = 2 + 4n$

(D) $a_n = 4 - 4n$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the sequence type and parameters

Determine the explicit formula

Answer: