What is the formula for the following geometric sequence?

3, 12, 48, 192, ...

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

Correct  a = 3 · 4⁽ⁿ ⁻ ¹⁾

Step-by-step explanation:

Given:

Geometric sequence 3, 12, 48, 192,

First term       a₁ = 3

Second term a₂ = 12

Third term     a₃ = 48

Common ratio or quotient:

q = a₂ / a₁ = a₃ / a₂ = 12 / 3 = 48 / 12 = 4

q = 4

First term       a₁ = 3

Second term a₂ = a · q

Third term     a₃ = a₂ · q = a₁ · q²

Fourth term a₄ = a₃ · q = a₁ · q³

n- th term aₙ = a₁ · q⁽ⁿ ⁻ ¹⁾

In this case  aₙ =  3 · 4⁽ⁿ ⁻ ¹⁾

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18. g

20. h 30 degree turn.

21. d 90 degree angles

and also 19 is a. a sphere not a cirlcle

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d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.