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

use the explicit formula to find $a_1$.
$a_1 = $

Question

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

use the explicit formula to find $a_1$.
$a_1 = $

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" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Sequence Notation" ] } ## Set up the equations for the given terms Using the *Arithmetic Sequences* knowledge point $$ \begin{aligned} a_n &= a_1 + (n - 1)d \ a_7 &= a_1 + 6d = 10.2 \ a_{12} &= a_1 + 11d = 17.7 \end{aligned} $$ ## Solve for the common difference d Using the *Arithmetic Sequences* knowledge point $$ \begin{aligned} (a_1 + 11d) - (a_1 + 6d) &= 17.7 - 10.2 \ 5d &= 7.5 \ d &= 1.5 \end{aligned} $$ ## Solve for the first term a_1 Using the *Arithmetic Sequences* knowledge point $$ \begin{aligned} a_1 + 6(1.5) &= 10.2 \ a_1 + 9 &= 10.2 \ a_1 &= 1.2 \end{aligned} $$ Use the explicit formula to find $a_1$. $a_1 =$ 1.2 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequences" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the equations for the given terms

Solve for the common difference d

Solve for the first term a_1

Answer: