Question

Find the 7th term in the sequence -1,2,-4,8

Answer 1

Answer:   -64

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Work Shown:

We have a geometric sequence

a = first term = -1

r = common ratio = (second term)/(first term) = 2/(-1) = -2

nth term

a(n) = a*(r)^(n-1)

a(n) = -1*(-2)^(n-1)

Now plug in n = 7 to get the 7th term

a(n) = -1*(-2)^(n-1)

a(7) = -1*(-2)^(7-1)

a(7) = -1*(-2)^6

a(7) = -1*(64)

a(7) = -64

The first seven terms are

-1, 2, -4, 8, -16, 32, -64

To get each new term, we multiply the last term by the common ratio -2

Answer 2

First, we need to find the rule for the sequence.
There’s not really an exact way to do this, you just have to look for a pattern.
This sequence follows the following notation:
An= -(-2^(n-1))
Then, we can plug 7 in for n.
A7 = -(-2^(n-1))
A7=-(-2^6)
A7=-64