Question

Write the explicit formula for the geometric sequence

Answer 1

The formula $3(4^{n-1})$ represents the geometric sequence.

Step-by-step explanation:

Step 1:

The value of $a_{n}$ is dependent on the value of n.

So n is independent while $a_{n}$ is dependent on n i.e. the value of $a_{n}$depends on the value of n.

Step 2:

We substitute the values of n in the functions to check which function satisfies the values of $a_{n}$.

If $n = 4, a_{n} = -4(3)^{n-1} = -4 (3^{3}) = -108.$ This does not equal the value of $a_{n}$.

If $n = 4, a_{n} = 4(3)^{n-1} =-4 (3^{3}) = 108.$ This does not equal the value of $a_{n}$.

If $n = 4, a_{n} =3(-4)^{n-1} = 3 (-4^{3}) = -192.$ This does not equal the value of $a_{n}$.

If $n = 4, a_{n} =3(4)^{n-1} = 3 (4^{3}) = 192.$ This equals the value of $a_{n}$.

So the fourth formula represents the geometric sequence.