Question

-3, -6, 12, -24,..... Recursive Formula an = an -1 -48an = an -1 . 2an = an -1 - 12an = - 3 . 2n -1

Answer 1

The recursive formula is;

`a_n=a_(n-1)\cdot2`

Step-by-step explanation:

The recursive formula for geometric progression can be written as;

`a_n=a_(n-1)\cdot r`

where r is the common difference.

Let us find the common difference of the given sequence;

`-3,-6,-12,-24,\ldots`
`\begin{gathered} r=(-6)/(-3)=(-12)/(-6) \\ r=2 \end{gathered}`

we can now substitute the value of r into the recursive formula;

`a_n=a_(n-1)\cdot2`

Therefore, the recursive formula is;

`a_n=a_(n-1)\cdot2`