Question

Find a recursive rule for the nth term of the sequence.7, 28, 112, 448, ...

Answer 1

Given the sequence 7, 28, 112, 448, ...

The sequence is a Geometric sequence because it has a common ratio

`Common\text{ ratio, r = }(28)/(7)=4`

First term, a = 4

`\begin{gathered} The\text{ nth term of a gp = ar}^(n-1) \\ Where\text{ n=number of terms} \\ a=\text{ first term } \\ r=common\text{ ratio} \end{gathered}`
`T_n=7\text{ \lparen4\rparen}^(n-1)`
`\begin{gathered} For\text{ recursive, } \\ T_n=r.T_(n-1) \\ T_n=4(T_(n-1)) \end{gathered}`
`The\text{ recursive rule is 4\lparen T}_(n-1))`