{[g(1)=51],[g(n)=g(n-1)+2]:} Find an explicit formula for g(n). g(n)=

Identify sequence type: Identify the type of sequence. The sequence is defined recursively with each term being 2 more than the previous term. This indicates that it is an arithmetic sequence.Determine first term and common difference: Determine the first term and the common difference. The first term g(1) is given as 51, and the common difference d is the amount added to each term to get the next term, which is 2.Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, which is g(n) = g(1) + (n-1)d. Substitute the values of g(1) and d into the formula. Here, g(1) = 51 and d = 2.Write explicit formula: Write the explicit formula by substituting the values from Step 3 into the formula. The explicit formula is g(n) = 51 + (n-1)×2.Simplify the formula: Simplify the formula. g(n) = 51 + 2n - 2, which simplifies to g(n) = 2n + 49.

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{[g(1)=51],[g(n)=g(n-1)+2]:}
Find an explicit formula for
g(n).

g(n)=

$\left\{\begin{array}{l} g(1)=51 \\ g(n)=g(n-1)+2 \end{array}\right.$ $\newline$ Find an explicit formula for $g(n)$ . $\newline$ $g(n)=$

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Algebra 2

Write a formula for an arithmetic sequence

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\left\{\begin{array}{l} g(1)=51 \\ g(n)=g(n-1)+2 \end{array}\right.

\newline

Find an explicit formula for

g(n)

\newline

g(n)=

Identify sequence type: Identify the type of sequence. The sequence is defined recursively with each term being $2$ more than the previous term. This indicates that it is an arithmetic sequence.
Determine first term and common difference: Determine the first term and the common difference. The first term $g(1)$ is given as $51$ , and the common difference $d$ is the amount added to each term to get the next term, which is $2$ .
Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, which is $g(n) = g(1) + (n-1)d$ . Substitute the values of $g(1)$ and $d$ into the formula. Here, $g(1) = 51$ and $d = 2$ .
Write explicit formula: Write the explicit formula by substituting the values from Step $3$ into the formula. The explicit formula is $g(n) = 51 + (n-1)\times2$ .
Simplify the formula: Simplify the formula. $g(n) = 51 + 2n - 2$ , which simplifies to $g(n) = 2n + 49$ .