Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary. 8,quad24,quad72,dots Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

Identify type of sequence: Identify the type of sequence. The given sequence is 8, 24, 72, ..., which is a geometric sequence because each term after the first is found by multiplying the previous term by a constant ratio.Determine common ratio: Determine the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term. r = 24 / 8 = 3Use formula for sum: Use the formula for the sum of the first n terms of a geometric series. The formula for the sum of the first n terms (S_n) of a geometric series is: S_n = (a_1 - a_1 * r^n) / (1 - r) where a_1 is the first term and r is the common ratio.Plug values into formula: Plug the values into the formula to find the sum of the first 7 terms. a_1 = 8 (the first term) r = 3 (the common ratio) n = 7 (the number of terms to sum) S_7 = (8 - 8 * 3^7) / (1 - 3)Calculate sum: Calculate the sum using the values from Step 4. S_7 = (8 - 8 * 3^7) / (1 - 3) S_7 = (8 - 8 * 2187) / (-2) S_7 = (8 - 17496) / (-2) S_7 = (-17488) / (-2) S_7 = 8744

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Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary.

8,quad24,quad72,dots
Sum of a finite geometric series:

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

Find the sum of the first $7$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $8, \quad 24, \quad 72, \ldots$ $\newline$ 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

7

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

\newline

8, \quad 24, \quad 72, \ldots

\newline

Sum of a finite geometric series:

\newline

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

\newline

Answer:

Identify type of sequence: Identify the type of sequence. $\newline$ The given sequence is $8, 24, 72, \ldots$ , which is a geometric sequence because each term after the first is found by multiplying the previous term by a constant ratio.
Determine common ratio: Determine the common ratio $r$ of the sequence. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ $r = \frac{24}{8} = 3$
Use formula for sum: Use the formula for the sum of the first $n$ terms of a geometric series. $\newline$ The formula for the sum of the first $n$ terms ( $S_n$ ) of a geometric series is: $\newline$ $S_n = \frac{a_1 - a_1 \cdot r^n}{1 - r}$ $\newline$ where $a_1$ is the first term and $r$ is the common ratio.
Plug values into formula: Plug the values into the formula to find the sum of the first $7$ terms. $a_1 = 8$ (the first term) $r = 3$ (the common ratio) $n = 7$ (the number of terms to sum) $S_7 = \frac{8 - 8 \times 3^7}{1 - 3}$
Calculate sum: Calculate the sum using the values from Step $4$ . $\newline$ $S_7 = \frac{(8 - 8 \times 3^7)}{(1 - 3)}$ $\newline$ $S_7 = \frac{(8 - 8 \times 2187)}{(-2)}$ $\newline$ $S_7 = \frac{(8 - 17496)}{(-2)}$ $\newline$ $S_7 = \frac{(-17488)}{(-2)}$ $\newline$ $S_7 = 8744$