Respuesta :

Numenius

The formula of a general term of a sequence is :

y_{n}=ar^{n-1}

Where a= first term, r = common ratio and n= number of terms.

Given first term: a = 2

We can find the common ratio by dividing second term by first term.

So, r= Second term/ first term= -8/2= -4

Next step is to plug in the values of a and r in the above formula to get the equation for geometric sequence.

So, y_{n}=2(-4)^{n-1} is the equation for a geometric sequence .

aachen
Given is a geometric sequence with a first term of 2 and a second term of -8.

we know the following facts about geometric sequence:-
first term = a
second term = a*r

So from the given information, we get
[tex]a = 2 \: \: and \: \: a \times r = - 8 \\ a = 2 \: \: and \: \: r = - 4[/tex]
we know that the general term of a geometric sequence is given by
[tex] a_{n} = a. {r}^{n - 1} [/tex]
So the final answer would be:-
[tex]a_{n} = 2 \times { (- 4)}^{n - 1} [/tex]

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