Consider the terms in the sequence: {1/3,1/9,1/27,…}

Common ratio of the sequence:
First term in the sequence:
recursive rule that describes the sequence:

1/3, 1/3, a×[r^(n-1)]

Step-by-step explanation:

First term is 1/3

Common ratio is the ratio of any two consecutive terms:

Term2/Term1 = (1/9)÷(1/3)

= (1/9)×(3/1)

= 1/3

Let a be the first term and r be the common ratio,

Then any term of the sequence can be obtained using the following formula:

a×[r^(n-1)]

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.