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

Question

03-11-2022
Mathematics

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

Sagot :

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CardenO361202 CardenO361202 · Answer 1 · 2022-11-03T05:37:09-04:00

Solution

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

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

[tex]Common\text{ ratio, r = }\frac{28}{7}=4[/tex]

First term, a = 4

[tex]\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}[/tex][tex]T_n=7\text{ \lparen4\rparen}^{n-1}[/tex][tex]\begin{gathered} For\text{ recursive, } \\ T_n=r.T_{n-1} \\ T_n=4(T_{n-1}) \end{gathered}[/tex][tex]The\text{ recursive rule is 4\lparen T}_{n-1})[/tex]

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