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Find the 11^th term of the geometric sequence
7,-21,63,dots
Answer:

Find the $11^{\text {th }}$ term of the geometric sequence $7,-21,63, \ldots$ $\newline$ Answer:

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Permutation and combination notation

Full solution

Q. Find the

11^{\text {th }}

term of the geometric sequence

7,-21,63, \ldots

\newline

Answer:

Identify common ratio: Identify the common ratio $r$ of the geometric sequence. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ $r = (-21) / 7 = -3$
Use formula for nth term: Use the formula for the nth term of a geometric sequence. $\newline$ The nth term $a_n$ of a geometric sequence can be found using the formula $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Substitute values for $11$ th term: Substitute the values into the formula to find the $11$ th term. $\newline$ $a_{11} = 7 \times (-3)^{11-1}$ $\newline$ $a_{11} = 7 \times (-3)^{10}$
Calculate $11$ th term: Calculate the $11$ th term. $\newline$ $a_{11} = 7 \times (59049)$ // $(-3)^{10} = 59049$ $\newline$ $a_{11} = 413343$

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