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What is the equation for a geometric sequence with a first term of 2 and a second term of -8

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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

a = 2 \: \: and \: \: a * r = - 8 \\ a = 2 \: \: and \: \: r = - 4
we know that the general term of a geometric sequence is given by

a_(n) = a. {r}^(n - 1)
So the final answer would be:-

a_(n) = 2 * { (- 4)}^(n - 1)
User Toldry
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3 votes

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 .

User Miski
by
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