What is the 6th term of the geometric sequence where a1 = 1,024 and a4 = –16?

Question

callisto · Answer

x r         x r       x r
a1 ---> a2 --->a3--->a4
So you can see if you want to get a4 from a1, you need to multiply a1 with r for 3 times
So a4 = a1 (r)^3
  -16 = 1024 (r)^3
  -1/64 = r^3
     r = -1/4
as you get the common ratio r,
you can apply the general formula to find the 6th term
T(n) = ar^(n-1) = 1024 (-1/4)^(6-1) = 1024*(-1/4)^5 = 1024*(-1/1024) = work it out yourself :)

callisto · Answer

@lgbasallote sorry but i think the general term you've written is wrong...

lgbasallote · Answer

oh yeah! geometric!!! so sorry...i am so screwed up @_@ i got confused hahaha lemme repeat that

lgbasallote · Answer

a6 = a1 r^(6-1)

first let us find r...

(((a1)r)r)r) = a4
ar^3 = -16
1024 r^3 = -16
r^3 = -16/1024
r^3 = -1/64
r = -1/4

a6 = 1024(-1/4)^5
a6 = 1024(-1/1024)
a6 = -1

better?

callisto · Answer

sure :)

anonymous · Answer

thank you so much for your help!!! means a lot!

callisto · Answer

(if you are talking to me) : You're welcome! Glad to help :D