Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary. 7,quad-35,quad175,dots Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

Identify Terms: Identify the first term (a_1) and the common ratio (r) of the geometric sequence. The first term a_1 is 7. To find the common ratio r, we divide the second term by the first term: r = -35 / 7 = -5.Use 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 = 7, a_1 = 7, and r = -5.Calculate Sum: Plug the values into the formula and calculate the sum. S_7 = (7 - 7 * (-5)^7) / (1 - (-5))Calculate Numerator: Calculate the numerator and the denominator separately. Numerator: 7 - 7 * (-5)^7 = 7 - 7 * (-78125) = 7 + 546875 Denominator: 1 - (-5) = 1 + 5 = 6Divide to Find Sum: Divide the numerator by the denominator to find the sum. S_7 = (7 + 546875) / 6 S_7 = 546882 / 6 S_7 = 91147

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

7,quad-35,quad175,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. $\newline$ $7, \quad-35, \quad 175, \ldots$ $\newline$ 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

7

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

\newline

7, \quad-35, \quad 175, \ldots

\newline

Sum of a finite geometric series:

\newline

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

\newline

Answer:

Identify Terms: Identify the first term $a_1$ and the common ratio $r$ of the geometric sequence. $\newline$ The first term $a_1$ is $7$ . To find the common ratio $r$ , we divide the second term by the first term: $r = -35 / 7 = -5$ .
Use 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, $n = 7$ , $a_1 = 7$ , and $r = -5$ .
Calculate Sum: Plug the values into the formula and calculate the sum. $S_7 = \frac{(7 - 7 \cdot (-5)^7)}{(1 - (-5))}$
Calculate Numerator: Calculate the numerator and the denominator separately. $\newline$ Numerator: $7 - 7 \times (-5)^7 = 7 - 7 \times (-78125) = 7 + 546875$ $\newline$ Denominator: $1 - (-5) = 1 + 5 = 6$
Divide to Find Sum: Divide the numerator by the denominator to find the sum. $\newline$ $S_7 = \frac{7 + 546875}{6}$ $\newline$ $S_7 = \frac{546882}{6}$ $\newline$ $S_7 = 91147$