Algebra 2 Test Questions on Writing Explicit Formulas

Question

Hey there! 👋 Algebra 2 can be tough, especially when writing explicit formulas. But don't worry, I've got you covered! This study guide breaks it down, and the quiz will help you test your knowledge. Let's ace this! 💯

christopher739 · Accepted Answer

📚 Quick Study Guide

🔢 Arithmetic Sequences: An arithmetic sequence has a constant difference ($d$) between consecutive terms. The explicit formula is $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term and $n$ is the term number.

➕ Geometric Sequences: A geometric sequence has a constant ratio ($r$) between consecutive terms. The explicit formula is $a_n = a_1 * r^{(n - 1)}$, where $a_1$ is the first term and $n$ is the term number.

💡 Identifying the Type of Sequence: Look for a constant difference to identify an arithmetic sequence or a constant ratio to identify a geometric sequence.

📝 Writing Explicit Formulas:
    *   Find the first term ($a_1$).
    *   Calculate the common difference ($d$) for arithmetic sequences or the common ratio ($r$) for geometric sequences.
    *   Substitute $a_1$, $d$ (or $r$) into the appropriate explicit formula.

🧮 Example - Arithmetic: For the sequence 2, 5, 8, 11..., $a_1 = 2$ and $d = 3$. The explicit formula is $a_n = 2 + (n-1)3$.

📈 Example - Geometric: For the sequence 3, 6, 12, 24..., $a_1 = 3$ and $r = 2$. The explicit formula is $a_n = 3 * 2^{(n-1)}$.

Practice Quiz

What is the explicit formula for the arithmetic sequence 7, 10, 13, 16...? 
    
        $a_n = 7 + 3n$
        $a_n = 4 + 3n$
        $a_n = 3 + 4n$
        $a_n = 7 + 4n$

What is the explicit formula for the geometric sequence 4, 8, 16, 32...? 
    
        $a_n = 4 * 2^n$
        $a_n = 2 * 2^n$
        $a_n = 4 * 2^{(n-1)}$
        $a_n = 2 * 4^{(n-1)}$

Given the arithmetic sequence with $a_1 = 5$ and $d = -2$, what is the explicit formula?
    
        $a_n = 5 - 2n$
        $a_n = 7 - 2n$
        $a_n = 3 - 2n$
        $a_n = -2 + 5n$

Given the geometric sequence with $a_1 = 2$ and $r = 3$, what is the explicit formula?
    
        $a_n = 2 * 3^n$
        $a_n = 3 * 2^{(n-1)}$
        $a_n = 2 * 3^{(n-1)}$
        $a_n = 3 * 2^n$

What is the explicit formula for the sequence -2, -4, -8, -16...? 
    
        $a_n = -2 * 2^{(n-1)}$
        $a_n = -2 + (-2)^{(n-1)}$
        $a_n = -1 * 2^n$
        $a_n = -4 * 2^{(n-1)}$

What is the explicit formula for the sequence 15, 12, 9, 6...? 
    
        $a_n = 18 - 3n$
        $a_n = 15 - 3n$
        $a_n = 12 + 3n$
        $a_n = 3n + 15$

The 5th term of an arithmetic sequence is 23 and the common difference is 5. Find the explicit formula.
    
        $a_n = 5n - 2$
        $a_n = 5n + 2$
        $a_n = 3n + 5$
        $a_n = 8 + 5n$

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Algebra 2 Test Questions on Writing Explicit Formulas

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