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What is the 9th term of the geometric sequence where a3=81 and r=3?

1 Answer

4 votes

Answer:


a_9=59049

Explanation:


\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^(n-1)$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}

Given:

  • a₃ = 81
  • r = 3

Substitute the given values into the formula and solve for a:


\begin{aligned}\implies a_3=a \cdot 3^(3-1)&=81\\a \cdot 3^2&=81\\a \cdot 9&=81\\a &=9\end{aligned}

Therefore, the equation for the nth term is:


\boxed{a_n=9 \cdot 3^(n-1)}

To find the 9th term, substitute n = 9 into the found equation:


\implies a_9=9 \cdot 3^(9-1)


\implies a_9=9 \cdot 3^(8)


\implies a_9=9 \cdot 6561


\implies a_9=59049

User Qasim Sarfraz
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