Question

What is an explicit formula for the geometric sequence -64,16,-4,1,... where the first term should be f(1).

Answer 1

Answer:

$a_{n} = -64(-\frac{1}{4})^{n-1}$

it seems like the first term is -64, so lets write the formula accordingly:

a_n = a1(r)^(n-1)

where 'n' is the number of terms

a1 is the first term of the sequence

'r' is the ratio

the ratio is $-\frac{1}{4}$ because -64 * $-\frac{1}{4}$ = 16 and so on...

the explicit formula is :

$a_{n}$ = $-64(-\frac{1}{4} )^{n-1}$