Question

Write a rule for the nth term of the sequence, then find a_7. 6, 24, 96, 384, ...

Answer 1

Given the sequence below,

$6,24,96,384,\ldots$

The sequence is a geometric sequence whose formula is given below as,

$Un_{}=ar^{n-1}$

To find the common ratio, r,

$\begin{gathered} r=\frac{2^{nd}\text{ term}}{1^{st}\text{ term}}\text{ or }\frac{3^{rd}\text{ term}}{2^{nd}\text{ term}} \\ \text{Where the 2}^{nd\text{ }}term=24,1^{st}\text{ term=6} \\ r=\frac{24}{6}=4 \end{gathered}$

To find the nth term of the sequence,

$\begin{gathered} \text{Where a=6 and r=4} \\ U_n=6(4)^{n-1} \end{gathered}$

To find the 7th,

$\begin{gathered} \text{Where n=7, a=6 and r=4} \\ U_7=6(4)^{7-1}=6(4)^6=6\times4096=24576 \end{gathered}$

Hence, the nth term is 6(4)ⁿ⁻¹ and

The 7th term is 24576