Question

Write an equation that models the sequence 6, 12, 24, 48

Answer 1

The recursive formula is

`a_n=2a_(n-1)`

and the explicit formula is

`a_n=6\cdot 2^(n-1)`

Explanation:

Given the sequence 6, 12, 24, 48.

In this sequence,

`a_1=6\\ \\a_2=12\\ \\a_3=24\\ \\a_4=48`

Note that

`12=2\cdot 6\Rightarrow a_2=2\cdot a_1\\ \\24=2\cdot 12\Rightarrow a_3=2\cdot a_2\\ \\48=2\cdot 24\Rightarrow a_4=2\cdot a_3`

Hence, the recursive formula is

`a_n=2a_(n-1)`

and the explicit formula is

`a_n=2^(n-1)\cdot a_1\\ \\a_n=6\cdot 2^(n-1)`