Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula. - 2, 6, - 18, 54, ...

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio, r. Considering the given sequence,

r = 6 / - 2 = - 18/6 = - 3

Therefore, the sequence is geometric.

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^ (n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = - 2

r = - 3

The explicit formula is

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

To find the 8th term, T8,

T8 = - 2 * ( - 3) ^ (8 - 1)

T8 = - 2 * ( - 3) ^7

T8 = - 2 * - 2187

T8 = 4374