Question

What is the 7th term of the geometric sequence where a1 = 1024 and a3 = 64?

Answer 1

do you know the formula ? :)

Answer 2

no sorry :(

Answer 3

You are dividing by 4 every time @Kreshnik

Answer 4

a4 = 16, a5 = 4, a6 = 1, a7 = 1/4 = 0.25

Answer 5

0.25 is the 7th term.

Answer 6

64/4 = 16, 16/4 = 4, 4/4 = 1, 1/4 = 0.25

Answer 7

Do you get it?

Answer 8

@coconut

\[\LARGE a_n=a_1\cdot r^{n-1}\]
let's substitute:
\[\LARGE a_3=1024\cdot r^{3-1}\]
\[\LARGE 64=1024\cdot r^2\]
\[\LARGE r^2=\frac{64}{1024}\]
\[\LARGE r^2=\frac{16}{256 }\]
\[\LARGE r^2=\frac{8}{128 }\]
\[\LARGE r^2=\frac{8}{128 }\]
\[\LARGE r^2=\frac{1}{16 }\]
\[\LARGE r^2=\frac{1}{4^2 }\]
\[\LARGE r^2=\left(\frac{1}{4 }\right)^2\]
\[\LARGE r=\frac14 \]

Answer 9

now you have:
\[\LARGE a_7=a_1\cdot r^{7-1}\]
\[\LARGE a_7=1024\cdot \left(\frac14 \right)^{6}\]
go for it...

Answer 10

@ParthKohli Yes Indeed 7th term is 0.25 ^^ Well done.