Answer:
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)
