{[g(1)=-19],[g(n)=g(n-1)+6]:} 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 6 more than the previous term, which indicates that it is an arithmetic sequence.Determine first term and common difference: Determine the first term and the common difference of the sequence. The first term g(1) is given as -19, and the common difference is the amount added to each term to get the next term, which is 6.Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, which is g(n) = g(1) + (n-1)d, where g(1) is the first term and d is the common difference. Here, g(1) = -19 and d = 6.Substitute values into formula: Substitute the values of g(1) and d into the formula to find the explicit formula for g(n). The formula becomes g(n) = -19 + (n-1)×6.Simplify the formula: Simplify the formula. Distribute the 6 into the parentheses: g(n) = -19 + 6n - 6.Combine like terms for final formula: Combine like terms to get the final explicit formula for the sequence. g(n) = 6n - 25.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

{[g(1)=-19],[g(n)=g(n-1)+6]:}
Find an explicit formula for
g(n).

g(n)=

$\left\{\begin{array}{l} g(1)=-19 \\ g(n)=g(n-1)+6 \end{array}\right.$ $\newline$ Find an explicit formula for $g(n)$ . $\newline$ $g(n)=$

View step-by-step help

Home

Math Problems

Algebra 2

Write a formula for an arithmetic sequence

Full solution

\left\{\begin{array}{l} g(1)=-19 \\ g(n)=g(n-1)+6 \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 $6$ more than the previous term, which indicates that it is an arithmetic sequence.
Determine first term and common difference: Determine the first term and the common difference of the sequence. The first term $g(1)$ is given as $-19$ , and the common difference is the amount added to each term to get the next term, which is $6$ .
Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, which is $g(n) = g(1) + (n-1)d$ , where $g(1)$ is the first term and $d$ is the common difference. Here, $g(1) = -19$ and $d = 6$ .
Substitute values into formula: Substitute the values of $g(1)$ and $d$ into the formula to find the explicit formula for $g(n)$ . The formula becomes $g(n) = -19 + (n-1)\times 6$ .
Simplify the formula: Simplify the formula. Distribute the $6$ into the parentheses: $g(n) = -19 + 6n - 6$ .
Combine like terms for final formula: Combine like terms to get the final explicit formula for the sequence. $g(n) = 6n - 25$ .