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)