Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 16,quad-8,quad4,dots Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

Identify Sequence Type: Identify the type of sequence. The given sequence is a geometric sequence because each term is obtained by multiplying the previous term by a common ratio (r).Determine First Term and Ratio: Determine the first term (a_1) and the common ratio (r). The first term a_1 is 16. To find the common ratio, divide the second term by the first term: r = (-8) / 16 = -1/2.Use Geometric Series Formula: Use the formula for the sum of the first n terms of a geometric series. The formula is S_n = (a_1 - a_1 * r^n) / (1 - r), where S_n is the sum of the first n terms, a_1 is the first term, r is the common ratio, and n is the number of terms.Plug Values into Formula: Plug the values into the formula to find the sum of the first 8 terms. S_8 = (16 - 16 * (-1/2)^8) / (1 - (-1/2))Calculate Sum: Calculate the sum. S_8 = (16 - 16 * (1/256)) / (1 + 1/2) S_8 = (16 - 1/16) / (3/2) S_8 = (256/16 - 1/16) / (3/2) S_8 = (255/16) * (2/3) S_8 = 255/24 S_8 = 10.625

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Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary.

16,quad-8,quad4,dots
Sum of a finite geometric series:

S_(n)=(a_(1)-a_(1)r^(n))/(1-r)
Answer:

Find the sum of the first $8$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $16, \quad-8, \quad 4, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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Q. Find the sum of the first

8

terms of the following sequence. Round to the nearest hundredth if necessary.

\newline

16, \quad-8, \quad 4, \ldots

\newline

Sum of a finite geometric series:

\newline

S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}

\newline

Answer:

Identify Sequence Type: Identify the type of sequence. $\newline$ The given sequence is a geometric sequence because each term is obtained by multiplying the previous term by a common ratio $r$ .
Determine First Term and Ratio: Determine the first term ( $a_1$ ) and the common ratio ( $r$ ). $\newline$ The first term $a_1$ is $16$ . To find the common ratio, divide the second term by the first term: $r = (-8) / 16 = -1/2$ .
Use Geometric Series Formula: Use the formula for the sum of the first $n$ terms of a geometric series. $\newline$ The formula is $S_n = \frac{a_1 - a_1 \cdot r^n}{1 - r}$ , where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of terms.
Plug Values into Formula: Plug the values into the formula to find the sum of the first $8$ terms. $S_8 = \frac{16 - 16 \times (-\frac{1}{2})^8}{1 - (-\frac{1}{2})}$
Calculate Sum: Calculate the sum. $\newline$ $S_8 = (16 - 16 \times (1/256)) / (1 + 1/2)$ $\newline$ $S_8 = (16 - 1/16) / (3/2)$ $\newline$ $S_8 = (256/16 - 1/16) / (3/2)$ $\newline$ $S_8 = (255/16) \times (2/3)$ $\newline$ $S_8 = 255/24$ $\newline$ $S_8 = 10.625$