Consider the arithmetic sequence below. -5, 4, 13, 22, 31, ...
Select all functions that define the given sequence.
O
f(n) = -5n+ 9
f(1) = -5, f(n) = f(n-1) + 7, for n 2 2
f(1) = -5, f(n) =- fin - 1) + 9, for n 22
f(1) = -5, f(n) = f(n-1) + 9, for n 2 2
0
f(n) = 9n - 14
f(n) = 9n - 5

c

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