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Find the sum of the first 10 terms of the following series, to the nearest integer.

6,36,216,dots
Answer:

Find the sum of the first $10$ terms of the following series, to the nearest integer. $\newline$ $6,36,216, \ldots$ $\newline$ Answer:

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Area and perimeter: word problems

Full solution

Q. Find the sum of the first

10

terms of the following series, to the nearest integer.

\newline

6,36,216, \ldots

\newline

Answer:

Recognize Pattern: Recognize the pattern in the series. $\newline$ The series $6$ , $36$ , $216$ , ... appears to be a geometric series where each term is multiplied by $6$ to get the next term. This means the common ratio ( $r$ ) is $6$ .
Identify Formula: Identify 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 of a geometric series is $S_n = \frac{a(1 - r^n)}{(1 - r)}$ , where $S_n$ is the sum of the first $n$ terms, $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms.
Plug in Values: Plug in the values into the formula. $\newline$ Here, $a = 6$ , $r = 6$ , and $n = 10$ . So, we have $S_{10} = 6(1 - 6^{10}) / (1 - 6)$ .
Calculate Sum: Calculate the sum using the formula. $\newline$ $S_{10} = 6(1 - 6^{10}) / (1 - 6)$ $\newline$ $S_{10} = 6(1 - 60466176) / (-5)$ $\newline$ $S_{10} = 6(-60466175) / (-5)$ $\newline$ $S_{10} = -362797050 / (-5)$ $\newline$ $S_{10} = 72559410$
Round to Integer: Round the sum to the nearest integer. $\newline$ The sum to the nearest integer is $72559410$ , which is already an integer, so no rounding is necessary.

More problems from Area and perimeter: word problems

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\newline

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A(d)=\pi d^{2}

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After the outbreak of a mysterious disease, the average wait time at a hospital increased by

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Question

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Question

The hypotenuse of a right triangle measures

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\newline

\square

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Question

One of the legs of a right triangle measures

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One of the legs of a right triangle measures

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and the other leg measures

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Question

Find the volume of a right circular cone that has a height of

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\newline

\mathrm{cm}^{3}

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Question

Find the volume of a right circular cone that has a height of

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\newline

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