Question

Formula for geometric sequence for 32, eight, two, 1/2

Answer 1

Formula for the geometric sequence is:

`a_n=32* ((1)/(4))^(n-1)\\`

Explanation:

Given geometric sequence:

`32,8,2,(1)/(2),..........n`

The formula for a geometric sequence to find the
`n`th term is given by:

`a_n=a_1* r^(n-1)\\`

Where
`a_n` represents the
`n`th term,
`a_1` represents first term and
`r` represents the common ratio between consecutive terms.

For the given sequence,

`a_1=32`

`r=(8)/(32)=(2)/(8)=(1)/(4)`

So, the formula for the sequence can be written as:

`a_n=32* ((1)/(4))^(n-1)\\`