Question

Question #479b0

Answer 1

`32, 16, 8; a_n=64(1/2)^(n-1)`

Explanation:

The variable `r` represents the common ratio, so this is a geometric sequence. In a geometric sequence, each term is multiplied by the common ratio `r` to obtain the next term. The first term is `64`, so we can find the next three terms by multiplying each previous one by `1/2`.

`a_1 => 64`
`a_2 => 64 * color(blue)(1/2) = 32`
`a_3 => 32 * color(blue)(1/2) = 16`
`a_4 => 16 * color(blue)(1/2) = 8`

The explicit formula of a geometric sequence is `a_n=a_1(r)^(n-1)`. Since `a_1=64` and `r=1/2`, we can substitute these numbers in.

`a_n=a_1(r)^(n-1)`
`a_n=64(1/2)^(n-1)`