what rule can be used to find the next term of the arithmetic sequence?
39, 60, 81, 102, 123, ...

$a_n = a_{n-1} - 39$
$a_n = a_{n-1} - 21$
$a_n = a_{n-1} + 21$
$a_n = a_{n-1} + 39$

the next term of the arithmetic sequence
39, 60, 81, 102, 123, ... is

Question

what rule can be used to find the next term of the arithmetic sequence?
39, 60, 81, 102, 123, ...

$a_n = a_{n-1} - 39$
$a_n = a_{n-1} - 21$
$a_n = a_{n-1} + 21$
$a_n = a_{n-1} + 39$

the next term of the arithmetic sequence
39, 60, 81, 102, 123, ... is

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequences", "Recursive Formulas" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Recursive Formulas" ] } ## Find the common difference Using the **Arithmetic Sequences** knowledge point $$ \begin{aligned} d &= 60 - 39 = 21 \ d &= 81 - 60 = 21 \ d &= 102 - 81 = 21 \ d &= 123 - 102 = 21 \end{aligned} $$ ## Determine the recursive rule Using the **Recursive Formulas** knowledge point $$ a_n = a_{n-1} + 21 $$ ## Calculate the next term Using the **Arithmetic Sequences** knowledge point $$ a_6 = 123 + 21 = 144 $$ ## Question 1 What rule can be used to find the next term of the arithmetic sequence? $39, 60, 81, 102, 123, \dots$ (A) $a_n = a_{n-1} - 39$

(B) $a_n = a_{n-1} - 21$

(C) $a_n = a_{n-1} + 21$

(D) $a_n = a_{n-1} + 39$ ## Question 2 The next term of the arithmetic sequence $39, 60, 81, 102, 123, \dots$ is 144. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequences" ] }

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QUESTION IMAGE

Question

Explanation:

Find the common difference

Determine the recursive rule

Calculate the next term

Answer:

Question 1

Question 2