g(n)=1+5(n-1) Complete the recursive formula of g(n). g(1)= g(n)=g(n-1)+

Identify First Term: Identify the first term of the sequence using the explicit formula. The explicit formula for the sequence is g(n) = 1 + 5(n - 1). To find the first term, g(1), we substitute n = 1 into the formula. g(1) = 1 + 5(1 - 1) g(1) = 1 + 5(0) g(1) = 1 + 0 g(1) = 1Determine Common Difference: Determine the common difference of the sequence. The sequence is defined by an arithmetic pattern where each term is 5 more than the previous term (since the coefficient of n in the explicit formula is 5). Therefore, the common difference, d, is 5.Write Recursive Formula: Write the recursive formula using the first term and the common difference. The recursive formula for an arithmetic sequence is g(n) = g(n - 1) + d, where d is the common difference. We have already determined that g(1) = 1 and d = 5. Therefore, the recursive formula is: g(n) = g(n - 1) + 5

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g(n)=1+5(n-1)
Complete the recursive formula of
g(n).

g(1)=

g(n)=g(n-1)+

$g(n)=1+5(n-1)$ $\newline$ Complete the recursive formula of $g(n)$ . $\newline$ g(1) = $\square$ $\newline$ g(n) = g(n-1)+$\square$

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Math Problems

Algebra 2

Write a formula for an arithmetic sequence

Full solution

g(n)=1+5(n-1)

\newline

Complete the recursive formula of

g(n)

\newline

g(1) = $\square$

\newline

g(n) = g(n-1)+$\square$

Identify First Term: Identify the first term of the sequence using the explicit formula. $\newline$ The explicit formula for the sequence is $g(n) = 1 + 5(n - 1)$ . To find the first term, $g(1)$ , we substitute $n = 1$ into the formula. $\newline$ $g(1) = 1 + 5(1 - 1)$ $\newline$ $g(1) = 1 + 5(0)$ $\newline$ $g(1) = 1 + 0$ $\newline$ $g(1) = 1$
Determine Common Difference: Determine the common difference of the sequence. $\newline$ The sequence is defined by an arithmetic pattern where each term is $5$ more than the previous term (since the coefficient of $n$ in the explicit formula is $5$ ). Therefore, the common difference, $d$ , is $5$ .
Write Recursive Formula: Write the recursive formula using the first term and the common difference. $\newline$ The recursive formula for an arithmetic sequence is $g(n) = g(n - 1) + d$ , where $d$ is the common difference. We have already determined that $g(1) = 1$ and $d = 5$ . $\newline$ Therefore, the recursive formula is: $\newline$ $g(n) = g(n - 1) + 5$