What is the 7th term of the geometric sequence where a1 = -2 and a5 = -512?

Question

espex · Answer

It will be interesting to see how you find the ratio without consecutive terms.

espex · Answer

$$a_n=a_1*r^{n-1}$$ So perhaps if you did, $$-2=1*r^{1-1}$$ you would get a ratio of -2?

anonymous · Answer

Here's how you do this problem:
First find the geometric mean of your a1 and a5 terms, geometric mean is calculated by taking the square root of the product of the two numbers
So the calculation for the geometric mean of a1 and a5 would be
(square root) (-2 times -512) = square root of 1024 = 32
32 is your a3 term
repeat this process to get a2 and a4
square root of -2 times 32 = 8
get the common ratio by diving a2/a1
your common ratio is 8/-2, which is -4
keep multiplying each term by this number to get the next term, and you will see it works out so that with this ratio, a1 will eventually become a5, and keep going two more times to get a7, you would get -8192, so that would be your final answer. Hope this helps.

espex · Answer

That does, it gives you a series of terms that will allow the use of $$a_n=a_1*r^{n-1}$$