Question

Write an expression for the general or nth term, an, for the geometric sequence. 1, -4, 16, -64...
A. An=1.(-4)^n-1
B. An=1.(-4)^n
C. An=1.4^n-1
D. An=1.4^n

Answer 1

so have you notice the common ratio
for example
what are the following equal to:
\[\frac{-4}{1}=? \\ \frac{16}{-4}=? \\ \frac{-64}{16}=?\]
notice I just did term/previous term

Answer 2

Is it 4?

Answer 3

you should find that those all equal to -4
which they should have term/previous term hold a constant number since they claimed it was a geometric sequence
but anyways since the common ratio is -4
you can definitely rule out C and D
and only look at A and B

Answer 4

Now the only way I can answer if it is A or B
is if you tell me if your class uses n=0 for the first term or you use n=1 for the first term

Answer 5

I bet it is n=1

Answer 6

but if you know this will really be needed because both of those could described the sequence depending on how n is defined

Answer 7

anyways if it is n=1
which of the following gives 1 as the answer:
\[A_1=1(-4)^{1-1} \text{ using choice A here } \\ A_1=1(-4)^{1} \text{ using choice B here }\]

Answer 8

we are looking to see which gives A_1 as 1
since 1 is the first number in the sequence

Answer 9

Okay, thanks. I think it's A.

Answer 10

yes that is only if your class uses n=1 to give first term