Year 11 Maths - General Number Patterns and Recursion

Geometric Sequences

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Questions

Question 1

30644

For the geometric sequence \(3,\,\,6,\,\,12,\,\, \ldots \), find the common ratio \((r)\) and the 5 th term.

Answer

\(r = 2,\,\,{T_5} = 48\)

Worked Solution

\begin{align}
&r=\frac{6}{3}=2 \\
&\begin{aligned}
T_{1} &=3 \\
T_{2} &=3 \times 2=6 \\
T_{3} &=3 \times 2 \times 2=12 \\
&=3 \times 2^{2}\\
T_{4} &=3 \times 2^{3} \\
T_{5} &=3 \times 2^{4} \\
&=48
\end{aligned}
\end{align}

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