Find an explicit formula for the geometric sequence (1)/(2),-4,32,-256,dots Note: the first term should be a(1). a(n)=

Sequence Type: We have the sequence: (1/2), -4, 32, -256, ... Is the given sequence geometric or arithmetic? (1/2), -4, 32, -256, ... Here, each term is multiplied by a common ratio. The given sequence is geometric.Determining a1 and r: Determine the values of a1 and r of the sequence. First term: a1 = 1/2 Common ratio: r = (-4)/(1/2) = -8Expression for an: Determine an expression to describe an. Substitute 1/2 for a1 and -8 for r. an = a1 (r)^(n - 1) an = (1/2)(-8)^(n-1)

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Find an explicit formula for the geometric sequence

(1)/(2),-4,32,-256,dots
Note: the first term should be
a(1).

a(n)=

Find an explicit formula for the geometric sequence $\newline$ $\frac{1}{2}, -4, 32, -256, \dots$ $\newline$ Note: the first term should be $a(1)$ . $\newline$ $a(n)=$

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Math Problems

Algebra 1

Write variable expressions for geometric sequences

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Q. Find an explicit formula for the geometric sequence

\newline

\frac{1}{2}, -4, 32, -256, \dots

\newline

Note: the first term should be

a(1)

\newline

a(n)=

Sequence Type: We have the sequence: $(\frac{1}{2}), -4, 32, -256, \ldots$ $\newline$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ $\newline$ $(\frac{1}{2}), -4, 32, -256, \ldots$ $\newline$ $\newline$ Here, each term is multiplied by a common ratio. $\newline$ $\newline$ The given sequence is geometric.
Determining $a_1$ and $r$ : Determine the values of $a_1$ and $r$ of the sequence. $\newline$ First term: $a_1 = \frac{1}{2}$ $\newline$ Common ratio: $r = \frac{-4}{\frac{1}{2}} = -8$
Expression for an: Determine an expression to describe $a_n$ .
Substitute $\frac{1}{2}$ for $a_1$ and $-8$ for $r$ .
$a_n = a_1 r^{(n - 1)}$
$a_n = \left(\frac{1}{2}\right)(-8)^{(n-1)}$