Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary. 20,quad-100,quad500,dots Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

Identify Terms and Ratio: Identify the first term (a_1) and the common ratio (r) of the geometric sequence. The first term a_1 is 20. To find the common ratio r, we divide the second term by the first term. r = (-100) / 20 = -5Use Sum Formula: Use the formula for the sum of the first n terms of a geometric series to find the sum of the first 9 terms. 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 and Calculate: Plug the values into the formula and calculate the sum. S_9 = (20 - 20 * (-5)^9) / (1 - (-5))Calculate Numerator and Denominator: Calculate the numerator and the denominator separately. First, calculate 20 * (-5)^9. (-5)^9 = -1953125 20 * (-5)^9 = -39062500 Now, calculate the denominator. 1 - (-5) = 1 + 5 = 6Complete Sum Calculation: Complete the calculation for the sum. S_9 = (20 - (-39062500)) / 6 S_9 = (20 + 39062500) / 6 S_9 = 39062520 / 6 S_9 ≈ 6510416.67

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Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary.

20,quad-100,quad500,dots
Sum of a finite geometric series:

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

Find the sum of the first $9$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $20, \quad-100, \quad 500, \ldots$ $\newline$ 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

9

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

\newline

20, \quad-100, \quad 500, \ldots

\newline

Sum of a finite geometric series:

\newline

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

\newline

Answer:

Identify Terms and Ratio: Identify the first term $a_1$ and the common ratio $r$ of the geometric sequence. $\newline$ The first term $a_1$ is $20$ . To find the common ratio $r$ , we divide the second term by the first term. $\newline$ $r = (-100) / 20 = -5$
Use Sum Formula: Use the formula for the sum of the first $9$ terms of a geometric series to find the sum of the first $9$ terms. $\newline$ 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 and Calculate: Plug the values into the formula and calculate the sum. $S_9 = \frac{(20 - 20 \cdot (-5)^9)}{(1 - (-5))}$
Calculate Numerator and Denominator: Calculate the numerator and the denominator separately. $\newline$ First, calculate $20 \times (-5)^9$ . $\newline$ $(-5)^9 = -1953125$ $\newline$ $20 \times (-5)^9 = -39062500$ $\newline$ Now, calculate the denominator. $\newline$ $1 - (-5) = 1 + 5 = 6$
Complete Sum Calculation: Complete the calculation for the sum. $\newline$ $S_9 = \frac{20 - (-39062500)}{6}$ $\newline$ $S_9 = \frac{20 + 39062500}{6}$ $\newline$ $S_9 = \frac{39062520}{6}$ $\newline$ $S_9 \approx 6510416.67$