Year 11 Maths - General Number Patterns and Recursion

Using a Recurrence Relation To Generate and Analyse an Geometric Sequence

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Questions

Question 1

30656

Given the recurrence relation \({t_1} = 250,\,\,{t_{n + 1}} = 1.1{t_n}\), calculate the value of the 6th term on the geometric sequence.

Answer

\(402.6275\)

Worked Solution

\begin{aligned}
t_{1} &=250\\
t_{2} &=250 \times 1.1 \\
t_{3} &=250 \times 1.1 \times 1.1 \\
&=250 \times(1.1)^{2} \\
t_{4} &=250 \times(1.1)^{3} \\
t_{n}&=250 \times(1.1)^{n-1} \\
t_{6}&=250 \times 1.1^{5} \\
&=402.6275
\end{aligned}

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