{[g(1)=-29],[g(n)=g(n-1)*(-4)]:} Find an explicit formula for g(n). g(n)=

Given Information: We are given that g(1) = -29 and that g(n) = g(n-1) * (-4) for n > 1. This is a recursive definition of the function g. To find an explicit formula, we need to determine how g(n) is related to the initial value g(1) when n increases.Identifying Pattern: Let's look at the first few terms to see if we can identify a pattern. We know g(1) = -29. Using the recursive formula: g(2) = g(1) * (-4) = -29 * (-4) = 116. g(3) = g(2) * (-4) = 116 * (-4) = -464.Geometric Sequence Analysis: We can see that each term is -4 times the previous term. This is a geometric sequence with the first term a = g(1) = -29 and common ratio r = -4. The nth term of a geometric sequence is given by the formula a * r^(n-1).Explicit Formula: Substituting the values of a and r into the formula for the nth term, we get: g(n) = -29 * (-4)^(n-1). This is the explicit formula for g(n).

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{[g(1)=-29],[g(n)=g(n-1)*(-4)]:}
Find an explicit formula for
g(n).

g(n)=

$\begin{cases} g(1)=-29, g(n)=g(n-1)\cdot(-4) \end{cases}$ Find an explicit formula for $g(n)$ . $g(n)=$

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Math Problems

Algebra 1

Write variable expressions for geometric sequences

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\begin{cases} g(1)=-29, g(n)=g(n-1)\cdot(-4) \end{cases}

Find an explicit formula for

g(n)

g(n)=

Given Information: We are given that $g(1) = -29$ and that $g(n) = g(n-1) \times (-4)$ for n > 1. This is a recursive definition of the function $g$ . To find an explicit formula, we need to determine how $g(n)$ is related to the initial value $g(1)$ when $n$ increases.
Identifying Pattern: Let's look at the first few terms to see if we can identify a pattern. We know $g(1) = -29$ . Using the recursive formula: $\newline$ $g(2) = g(1) \times (-4) = -29 \times (-4) = 116$ . $\newline$ $g(3) = g(2) \times (-4) = 116 \times (-4) = -464$ .
Geometric Sequence Analysis: We can see that each term is $-4$ times the previous term. This is a geometric sequence with the first term $a = g(1) = -29$ and common ratio $r = -4$ . The $n$ th term of a geometric sequence is given by the formula $a \cdot r^{(n-1)}$ .
Explicit Formula: Substituting the values of $a$ and $r$ into the formula for the $n$ th term, we get: $\newline$ $g(n) = -29 \cdot (-4)^{(n-1)}$ . $\newline$ This is the explicit formula for $g(n)$ .