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=(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*4096=24576 \end{gathered}`

Hence, the nth term is 6(4)ⁿ⁻¹ and

The 7th term is 24576