Find an explicit formula for the geometric sequence -8,-40,-200,-1000,dots.. Note: the first term should be c(1). c(n)=

Identify pattern and type: Identify the pattern in the sequence and determine if it is arithmetic or geometric. The given sequence is -8, -40, -200, -1000, ... To determine if the sequence is arithmetic or geometric, we look at the ratio of consecutive terms. -40 / -8 = 5 -200 / -40 = 5 -1000 / -200 = 5 Since each term is multiplied by the same number to get the next term, the sequence is geometric.Find first term and common ratio: Find the first term (c(1)) and the common ratio (r) of the sequence. The first term c(1) is given as -8. To find the common ratio, we divide the second term by the first term: r = -40 / -8 = 5Write explicit formula: Write the explicit formula for the geometric sequence using c(1) and r. The explicit formula for a geometric sequence is given by: c(n) = c(1) * r^(n - 1) Substitute c(1) = -8 and r = 5 into the formula: c(n) = -8 * 5^(n - 1)

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Find an explicit formula for the geometric sequence
-8,-40,-200,-1000,dots.. Note: the first term should be
c(1).

c(n)=

Find an explicit formula for the geometric sequence $-8,-40,-200,-1000,\ldots$ . Note: the first term should be $c(1)$ . $\newline$ $c(n)=$

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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

-8,-40,-200,-1000,\ldots

. Note: the first term should be

c(1)

\newline

c(n)=

Identify pattern and type: Identify the pattern in the sequence and determine if it is arithmetic or geometric. $\newline$ The given sequence is $-8, -40, -200, -1000, \ldots$ $\newline$ To determine if the sequence is arithmetic or geometric, we look at the ratio of consecutive terms. $\newline$ $\frac{-40}{-8} = 5$ $\newline$ $\frac{-200}{-40} = 5$ $\newline$ $\frac{-1000}{-200} = 5$ $\newline$ Since each term is multiplied by the same number to get the next term, the sequence is geometric.
Find first term and common ratio: Find the first term $c(1)$ and the common ratio $r$ of the sequence. $\newline$ The first term $c(1)$ is given as $-8$ . $\newline$ To find the common ratio, we divide the second term by the first term: $\newline$ $r = \frac{-40}{-8} = 5$
Write explicit formula: Write the explicit formula for the geometric sequence using $c(1)$ and $r$ . $\newline$ The explicit formula for a geometric sequence is given by: $\newline$ $c(n) = c(1) \cdot r^{(n - 1)}$ $\newline$ Substitute $c(1) = -8$ and $r = 5$ into the formula: $\newline$ $c(n) = -8 \cdot 5^{(n - 1)}$