Question

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

Answer 1

`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`