Question

Write a recursive formula for the sequence below. Use the variable "n" for your formula in your answer.

{2, -8, 32, -128, 512, ... }

Answer 1

`\begin{cases}a_1 = 2\\\\a_(n) = -4*a_(n-1)\end{cases}`

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Step-by-step explanation:

The first line of the answer says "the first term is 2".

The second line says "take any term and multiply by -4 to get the next term".

The
`a_n` represents the nth term while
`a_(n-1)` is the term just before it.

The second line shown above is the same as writing
`a_(n+1) = -4*a_n`

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The -4 is found by dividing any term over its previous one

-8/2 = -4

32/(-8) = -4

-128/32 = -4

512/(-128) = -4

This shows the common ratio is -4 and this sequence is geometric.