Question

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

Answer 1

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)`

Answer 2

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 .