The formula for any geometric sequence is an = a1 · rn - 1, where an represents the value of the nth term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the sequence - 3, - 6, - 12, - 24, ... ?

an = - 2 · (-3) n - 1

an = 2 · (-3) n - 1

an = - 3 · 2 n - 1

an = - 3 · (-2) n - 1

Answer: an = - 3 · 2^n - 1

Step-by-step explanation:

In a geometric series, the consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as

an = a1 * r^ (n - 1)

Where

a1 represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

Looking at the given sequence,

a = - 3

r = - 6 / - 3 = 2

Therefore, the formula for the sequence is

an = - 3 * 2^ (n - 1)

an = - 3. 2n - 1

Step-by-step explanation:

From the given sequence, the value of the first term, a1 = - 3

r = common ratio = the ratio of the second term, a2 to the first term, a1

From the given sequence, a2 = - 6

and a1 = - 3

-6 : - 3 = - 6/-3 = 2

The common ratio, r = 2

In the formula, an = a1. rn - 1,

we substitute the values of a1 and r

an = - 3. 2n - 1