What is the 20th term of the sequence that begins -2, 4, -8, 16...?

Question

eskelle · Answer

options are 
a. 2,097,152
b. 524,288
c. -524,288
d. 1,048,576

eskelle · Answer

please explain or show how to get answer?

peachpi · Answer

this is a geometric sequence since each term is -2 times the previous term. This is the formula for a geometric sequence
$$a_n=a_1r^{n-1}$$

r = the common ratio (what you're multiplying by)
a_1 = first term = -2

So the equation for your sequence is $$a_n=-2(-2)^{n-1}$$

Then you'd plug in 20 for n to find the 20th term

eskelle · Answer

so a(20)=-2(-2)^20-1? how do you evaluate the rest?

peachpi · Answer

stick that in a calculator.

eskelle · Answer

i got 1,048,576.  so d is correct?

eskelle · Answer

thank you :)