Question

What is the 7th term of a geometric sequence where a1=256 and a3=16?

Answer 1

I fiddled around with the problem for a while but no, just find the formula:


`a_n=256\left((1)/(4)\right)^(n-1)`

The ratio is 1/4 because:
4^4 = 256 =
`a_1`
4^2 = 16 =
`a_3`

First element of sequence: 256
So with these two numbers you can get the formula.

Now plug in 7 for n and solve.


`a_7 = 256( (1)/(4))^(7-1) = 256( (1)/(4))^(6) = (256)/(4096) = (1)/(16)`

Answer 2

The answer is 0.0625