Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 100,quad88,quad77.44,dots Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

Identify common ratio: First, we need to identify the common ratio (r) of the geometric sequence. We can find this by dividing the second term by the first term. r = 88 / 100 = 0.88Use sum formula: Next, we use the formula for the sum of the first n terms of a geometric series: 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 in values: We plug in the values we know into the formula: S_8 = (100 - 100 * 0.88^8) / (1 - 0.88)Calculate the sum: Now we calculate the sum using the values: S_8 = (100 - 100 * 0.88^8) / (1 - 0.88) S_8 = (100 - 100 * 0.23357214690901212) / 0.12 S_8 = (100 - 23.357214690901212) / 0.12 S_8 = (76.64278530909879) / 0.12 S_8 = 638.6898775758232Round the sum: Finally, we round the sum to the nearest hundredth: S_8 ≈ 638.69

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

100,quad88,quad77.44,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. $\newline$ $100, \quad 88, \quad 77.44, \ldots$ $\newline$ 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

100, \quad 88, \quad 77.44, \ldots

\newline

Sum of a finite geometric series:

\newline

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

\newline

Answer:

Identify common ratio: First, we need to identify the common ratio $r$ of the geometric sequence. We can find this by dividing the second term by the first term. $r = \frac{88}{100} = 0.88$
Use sum formula: Next, we use the formula for the sum of the first $n$ terms of a geometric series: $S_n = \frac{a_1 - a_1 \cdot r^n}{1 - r}$ 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 in values: We plug in the values we know into the formula: $S_8 = \frac{(100 - 100 \times 0.88^8)}{(1 - 0.88)}$
Calculate the sum: Now we calculate the sum using the values: $\newline$ $S_8 = \frac{100 - 100 \times 0.88^8}{1 - 0.88}$ $\newline$ $S_8 = \frac{100 - 100 \times 0.23357214690901212}{0.12}$ $\newline$ $S_8 = \frac{100 - 23.357214690901212}{0.12}$ $\newline$ $S_8 = \frac{76.64278530909879}{0.12}$ $\newline$ $S_8 = 638.6898775758232$
Round the sum: Finally, we round the sum to the nearest hundredth: $S_8 \approx 638.69$