Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 9,quad-12,quad16,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 9. To find the common ratio r, we divide the second term by the first term: r = -12 / 9 = -4/3.Use sum formula: 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). Here, n = 8, a_1 = 9, and r = -4/3.Substitute and calculate sum: Substitute the values into the formula and calculate the sum. S_8 = (9 - 9 * (-4/3)^8) / (1 - (-4/3))Calculate (-4/3)^8: Calculate the value of (-4/3)^8. (-4/3)^8 = (-4)^8 / 3^8 = 65536 / 6561Substitute value into formula: Substitute the value of (-4/3)^8 into the sum formula. S_8 = (9 - 9 * (65536 / 6561)) / (1 + 4/3)Simplify expression: Simplify the expression. S_8 = (9 - 9 * (65536 / 6561)) / (7/3) S_8 = (9 - 59049 / 6561) / (7/3)Calculate numerator: Calculate the numerator of the sum. 9 - 59049 / 6561 = 9 - 9 = 0

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

9,quad-12,quad16,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. $\newline$ $9, \quad-12, \quad 16, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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Math Problems

Algebra 2

Sum of finite series not start from 1

Full solution

Q. Find the sum of the first

8

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

\newline

9, \quad-12, \quad 16, \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 $9$ . To find the common ratio $r$ , we divide the second term by the first term: $r = -12 / 9 = -4/3$ .
Use sum formula: Use the formula for the sum of the first $n$ terms of a geometric series: $S_n = \frac{a_1 - a_1 \cdot r^n}{1 - r}$ . Here, $n = 8$ , $a_1 = 9$ , and $r = -\frac{4}{3}$ .
Substitute and calculate sum: Substitute the values into the formula and calculate the sum. $\newline$ $S_8 = \frac{9 - 9 \times (-\frac{4}{3})^8}{1 - (-\frac{4}{3})}$
Calculate $(-\frac{4}{3})^8$ : Calculate the value of $(-\frac{4}{3})^8.$ $\newline$ $(-\frac{4}{3})^8 = (-4)^8 / 3^8 = \frac{65536}{6561}$
Substitute value into formula: Substitute the value of $(-\frac{4}{3})^8$ into the sum formula. $\newline$ $S_8 = \frac{9 - 9 \times (\frac{65536}{6561})}{1 + \frac{4}{3}}$
Simplify expression: Simplify the expression. $\newline$ $S_8 = \frac{9 - 9 \times \left(\frac{65536}{6561}\right)}{\frac{7}{3}}$ $\newline$ $S_8 = \frac{9 - \frac{59049}{6561}}{\frac{7}{3}}$
Calculate numerator: Calculate the numerator of the sum. $\newline$ $9 - \frac{59049}{6561} = 9 - 9 = 0$