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Find the sum of the first 9 terms of the following series, to the nearest integer.

22,44,88,dots
Answer:

Find the sum of the first $9$ terms of the following series, to the nearest integer. $\newline$ $22,44,88, \ldots$ $\newline$ Answer:

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Geometric sequences

Full solution

Q. Find the sum of the first

9

terms of the following series, to the nearest integer.

\newline

22,44,88, \ldots

\newline

Answer:

Identify type of series: Identify the type of series. $\newline$ The given series is $22, 44, 88, \ldots$ , which appears to be a geometric series because each term is obtained by multiplying the previous term by a constant.
Determine common ratio: Determine the common ratio $r$ of the series. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ $\frac{44}{22} = 2$ $\newline$ Common Ratio $r$ : $2$
Use formula for sum: Use 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 ( $S_n$ ) of a geometric series is: $\newline$ $S_n = a \cdot (1 - r^n) / (1 - r)$ , where $a$ is the first term and $r$ is the common ratio.
Calculate sum of terms: Calculate the sum of the first $9$ terms. $\newline$ First term $(a) = 22$ $\newline$ Common ratio $(r) = 2$ $\newline$ Number of terms $(n) = 9$ $\newline$ $S_9 = 22 \times (1 - 2^9) / (1 - 2)$
Perform calculations: Perform the calculations. $\newline$ $S_9 = 22 \times (1 - 512) / (1 - 2)$ $\newline$ $S_9 = 22 \times (-511) / (-1)$ $\newline$ $S_9 = 22 \times 511$ $\newline$ $S_9 = 11242$

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