Given that a3 = 12 and a5 = 48, find the explicit rule for the geometric sequence, given that the common ratio is positive

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

= a

where a is the first term and r the common ratio, thus

= ar² = 12 → (1)

= a = 48 → (2)

Divide (2) by (1)

= = 4

r² = 4 ⇒ r = ± 2 ⇒ r = 2 ← since r > 0

Substitute r = 2 into (1) for corresponding value of a

4a = 12 ⇒ a = 3

Hence

= 3 ← explicit rule

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

she was supposed to add the hours(38.5) and multiply the amount of money she earned(7.50) resulting in $288.75 .

correct me if i'm wrong and if it is i'm truly sorry.