Question

Write the explicit formula that represents the geometric sequence -2, 8, -32, 128

I tried this one and this is what I goy. Probably is wrong
a^n= -2^1 * -4^n-1

The arrows up means pointed down but I couldn't find any that pointed down except gpt the up n-1

Answer 1

Well I see you noticed that the geometric sequence can be represented by powers of 2.
-2 = (-1)^1*2^1
8 = (-1)^2*2^3
-32= (-1)^3*2^5
128= (-1)^4*2^7
Can you get the general formula from here ?

Answer 2

Sorry trying to write it all down. I don't really understand it. I see the numbers getting higher but don't get how

Answer 3

Ok if you look closely you'll see that the exponent of (-1) equals the number of the term and the exponent of 2 can be written like:
1 = 2*1 - 1
3 = 2*2 - 1
5 = 2*3 - 1

a1 = -2 = (-1)^1 * 2^1
a2 = 8 = (-1)^2 * 2^3
a3 = -32 = (-1)^3 * 2^5
a4 = 128 = (-1)^4 * 2^7
And so you'll get :
an = (-1)^n * 2^(2n-1)

Answer 4

I think I get it. But how did you get the (2n-1) part? To add the 2 in front of it why not just n-1

Answer 5

n-1 would give you for each term
1-1 = 0
2-1 = 1...
which are not the right exponents of 2 in the sequence. I'm afraid there isn't really a rule on how to find general terms, you'll just have to use your instincts. Notice how the terms change in function of n. In this case we just had to find the exponents of 2 (1, 3, 5, 7, ....) in function of n.

Answer 6

Got it now. Hopefully wont need to ask again with this kind of question.
Thanks a lot for helping. Happy Holidays.

Answer 7

You're much welcome. Happy holidays to you too =)