Question

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 1

Answer:

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

Answer 2

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)