{[g(1)=2.2],[g(n)=g(n-1)*(-5)]:} Find an explicit formula for g(n). g(n)=

Initial Condition: The problem gives us the initial condition g(1) = 2.2 and a recursive formula g(n) = g(n-1) * (-5). To find an explicit formula for g(n), we need to express g(n) in terms of n without the need for previous terms.Apply Recursive Formula: Let's start by applying the recursive formula to the first few terms to see if we can identify a pattern. g(1) = 2.2 g(2) = g(1) * (-5) = 2.2 * (-5) g(3) = g(2) * (-5) = (2.2 * (-5)) * (-5) We can see that each term is the previous term multiplied by -5.Express in Terms of n: Now let's express g(n) in terms of g(1): g(2) = g(1) * (-5) g(3) = g(2) * (-5) = g(1) * (-5)^2 g(4) = g(3) * (-5) = g(1) * (-5)^3 ... g(n) = g(1) * (-5)^(n-1)Substitute Value into Formula: Since we know g(1) = 2.2, we can substitute this value into our formula: g(n) = 2.2 * (-5)^(n-1) This is the explicit formula for g(n).

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{[g(1)=2.2],[g(n)=g(n-1)*(-5)]:}
Find an explicit formula for
g(n).

g(n)=

$\begin{cases} g(1)=2.2, g(n)=g(n-1)\cdot(-5) \end{cases}$ Find an explicit formula for $g(n)$ . $g(n)=$

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Math Problems

Algebra 1

Write variable expressions for geometric sequences

Full solution

\begin{cases} g(1)=2.2, g(n)=g(n-1)\cdot(-5) \end{cases}

Find an explicit formula for

g(n)

g(n)=

Initial Condition: The problem gives us the initial condition $g(1) = 2.2$ and a recursive formula $g(n) = g(n-1) \times (-5)$ . To find an explicit formula for $g(n)$ , we need to express $g(n)$ in terms of $n$ without the need for previous terms.
Apply Recursive Formula: Let's start by applying the recursive formula to the first few terms to see if we can identify a pattern. $\newline$ $g(1) = 2.2$ $\newline$ $g(2) = g(1) \times (-5) = 2.2 \times (-5)$ $\newline$ $g(3) = g(2) \times (-5) = (2.2 \times (-5)) \times (-5)$ $\newline$ We can see that each term is the previous term multiplied by $-5$ .
Express in Terms of n: Now let's express $g(n)$ in terms of $g(1)$ :
$g(2) = g(1) \times (-5)$
$g(3) = g(2) \times (-5) = g(1) \times (-5)^2$
$g(4) = g(3) \times (-5) = g(1) \times (-5)^3$
...
$g(n) = g(1) \times (-5)^{(n-1)}$
Substitute Value into Formula: Since we know $g(1) = 2.2$ , we can substitute this value into our formula: $g(n) = 2.2 \times (-5)^{(n-1)}$ This is the explicit formula for $g(n)$ .