Question

Find the indicated nth term of the geometric sequence.
6th term:
a[5]=3/256, a[8]=-3/16,384

Answer 1

Does a[5] mean that it is the 5th term?

Answer 2

what is 384?

Answer 3

Assuming that a[5] means the 5th term, I am going to make it the 1st term and a[8] the 4th term. going by the Geometric Sequence formula
a[n]=a1]*r^(n-1) , where r is the common ratio, then
a[4]=a[1]*r*(4-1)
-3/16/384=3/256*r^3
Multiplying both sides by 256/3, the result is
-1/64=r^3
Now finding the cubic root on both side , the result is r=-1/4. to find the sixth term (or in this case the second term) using the formula again
a[6] equivalent to a[2]=a[1]*(-1/4)^(2-1)
a[6] =(3/256)*(-1/4)=-3/1024

Answer 4

oh ok thank you! this makes perfect sense!