The sum of a geometric sequence is a(1-rn)/(1-r)
In this case, a = 8, r = -2 and n=15
So the sum is 8(1-(-2)15)/(1+2)
=8(1+32768)/3
=87,384
So the sum of the first 15 terms of the sequence 8, -16, 32, -64.... is 87,384.
Yes, that's what a geometric sequence is about.
yes
The terms are: 4, 8 and 16
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.
No. Although the ratios of the terms in the Fibonacci sequence do approach a constant, phi, in order for the Fibonacci sequence to be a geometric sequence the ratio of ALL of the terms has to be a constant, not just approaching one. A simple counterexample to show that this is not true is to notice that 1/1 is not equal to 2/1, nor is 3/2, 5/3, 8/5...
Yes, that's what a geometric sequence is about.
A descending geometric sequence is a sequence in which the ratio between successive terms is a positive constant which is less than 1.
yes
A static sequence: for example a geometric sequence with common ratio = 1.
FALSE (Apex)
Ratio
It is 4374
The terms are: 4, 8 and 16
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.
No. Although the ratios of the terms in the Fibonacci sequence do approach a constant, phi, in order for the Fibonacci sequence to be a geometric sequence the ratio of ALL of the terms has to be a constant, not just approaching one. A simple counterexample to show that this is not true is to notice that 1/1 is not equal to 2/1, nor is 3/2, 5/3, 8/5...
They are 14, 42, 126, 378 and 1134.
It is a constant, other than 0 or 1.