{3, 6, 9, 12, 15, 18, 21, ...)

Below

Step-by-step explanation:

5)

The sequence includes the terms 3,6,9,12,15.. and so on

Notice that each time we add 3.

The first term is 3.

We can see it in a different way

● 3 = 3×1

● 6 = 3×2

● 9 = 3×3

● 12 = 3×4

Let 1 be n. Notice what happens

● 3 = 3n

● 6 = 3 × (n+1)

● 9 = 3 × (n+2)

● 12 = 3 × (n+3)

So we can express it as.

● a1 = 3 × 1 =3

● a2 = 3×2 =6

● a3 = 3×3 = 9

So the third term is a3 wich is 9

● a6 = 3×6 = 18

So the sixth term is 18 .

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6)

the sequence is defined by:

● f(n-1) = -0.5 f(n)

Repalce n-1 with n and n with n+1

● f(n) = -0.5 f(n+1)

So to get a term you must multiply the next one by -0.5

The first term in the sequence is 120.

● 120 = -0.5 f(n+1)

● f(n+1) = 120/-0.5

● f(n+1) = -60

So the second term is -60

50- 250 is correct i did that one too

step-by-step explanation:

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