What is the formula for the following geometric sequence? 3, 12, 48, 192, ...

an = 4 · 3n - 1
an = 3 · (-4)n - 1
an = 3 · 4n - 1
an = (1/4) · 3n - 1

answer: 60

step-by-step explanation:

1/2a + (2/3×30)   = 50

1/2a + 20 = 50

1/2a = 30

a = 60

answer: kljdcdhjbdlchjad oac apoich a

step-by-step explanation:

the answer is 24

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4