Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula. 3, - 18, 108, - 648,

a.) Yes it is a geometric sequence and common ratio = - 6

b.) 8th term = - 839808

c.) explicit formula = 3 * (-6^n-1)

Step-by-step explanation:

Geometric sequences are defined by the formula ar^n-1

Where a is the first term,

r is the common ratio

n is the number of term.

a.) To check if the given series is a geometric progression, we divide 3rd term by 2nd term, and divide 4th term by 3rd them. If we get the same answer, then it is a geometric progression and this answer is the common ratio

The terms are 3, - 8, 108, - 648

3rd term/2nd term = 108/-18 = - 6

4th term/3rd term = - 648/108 = - 6.

Since both answers are equal, Then the progression is a geometric progression Where a, first term = 3 and common ratio = - 6

b) for 8th term, the geometric formula is denoted by: ar^8-1

=3 * (-6^7) = - 839808

c.) explicit formula = 3 * (6^n-1)