writing an explicit formula for an arithmetic sequence when given two terms

the seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7.

what is the common difference of the arithmetic sequence?
the common difference is

Question

writing an explicit formula for an arithmetic sequence when given two terms

the seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7.

what is the common difference of the arithmetic sequence?
the common difference is

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequences", "Slope Formula" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Slope Formula", "Common Difference" ] } ## Set up the sequence equations Using the *Arithmetic Sequences* knowledge point $$ \begin{aligned} a_7 &= a_1 + 6d = 10.2 \ a_{12} &= a_1 + 11d = 17.7 \end{aligned} $$ ## Solve for the common difference Using the *Slope Formula* knowledge point $$ \begin{aligned} d &= \frac{a_{12} - a_7}{12 - 7} \ d &= \frac{17.7 - 10.2}{5} \ d &= \frac{7.5}{5} = 1.5 \end{aligned} $$ The seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7. What is the common difference of the arithmetic sequence? The common difference is 1.5 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequences" ] }

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Question

Explanation:

Set up the sequence equations

Solve for the common difference

Answer: